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    <title>MaplePrimes - Questions and Posts tagged with constants</title>
    <link>http://www.mapleprimes.com/tags/constants</link>
    <language>en-us</language>
    <copyright>2012 Maplesoft, A Division of Waterloo Maple Inc.</copyright>
    <generator>Maplesoft Document System</generator>
    <lastBuildDate>Mon, 21 May 2012 16:15:53 GMT</lastBuildDate>
    <pubDate>Mon, 21 May 2012 16:15:53 GMT</pubDate>
    <itunes:subtitle />
    <itunes:summary />
    <description>The most recent questions and posts on MaplePrimes tagged with constants</description>
    <image>
      <url>http://www.mapleprimes.com/images/mapleprimeswhite.jpg</url>
      <title>MaplePrimes - Questions and Posts tagged with constants</title>
      <link>http://www.mapleprimes.com/tags/constants</link>
    </image>
    <item>
      <title>MRB constant N part 3</title>
      <link>http://www.mapleprimes.com/posts/134388-MRB-Constant-N-Part-3?ref=Feed:MaplePrimes:Tagged With constants</link>
      <itunes:summary>&lt;p&gt;&amp;nbsp;&lt;/p&gt;
</itunes:summary>
      <description>&lt;p&gt;&amp;nbsp;&lt;/p&gt;
</description>
      <guid>134388</guid>
      <pubDate>Mon, 21 May 2012 01:30:50 Z</pubDate>
      <itunes:author>Marvin Ray Burns</itunes:author>
      <author>Marvin Ray Burns</author>
    </item>
    <item>
      <title>over defined problem</title>
      <link>http://www.mapleprimes.com/questions/134290-Over-Defined-Problem?ref=Feed:MaplePrimes:Tagged With constants</link>
      <itunes:summary>&lt;p&gt;&amp;nbsp;Have to solve and ODE in the domain of [-infnity +infinity ] via specific analytical method but due to some restrictions it could not be solved. In order to solve it, I have separated the domain into [-infinity 0 ] and [0 infinity]. So, I have to add some boundary values at x=0 to the problem. Assuming the solution of the mentioned ODE in &amp;nbsp;[-infinity 0 ] is g(x) and in [0 infinity]&amp;nbsp; is f(x), I added the boundary values of f(0)=g(0)=a and f ' (0)=b and obtained f(x...</itunes:summary>
      <description>&lt;p&gt;&amp;nbsp;Have to solve and ODE in the domain of [-infnity +infinity ] via specific analytical method but due to some restrictions it could not be solved. In order to solve it, I have separated the domain into [-infinity 0 ] and [0 infinity]. So, I have to add some boundary values at x=0 to the problem. Assuming the solution of the mentioned ODE in &amp;nbsp;[-infinity 0 ] is g(x) and in [0 infinity]&amp;nbsp; is f(x), I added the boundary values of f(0)=g(0)=a and f ' (0)=b and obtained f(x...</description>
      <guid>134290</guid>
      <pubDate>Wed, 16 May 2012 20:02:29 Z</pubDate>
      <itunes:author>farazhedayati</itunes:author>
      <author>farazhedayati</author>
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    <item>
      <title>MRB Constant Y</title>
      <link>http://www.mapleprimes.com/posts/133548-MRB-Constant-Y?ref=Feed:MaplePrimes:Tagged With constants</link>
      <itunes:summary>&lt;p&gt;&amp;nbsp;&lt;/p&gt;
</itunes:summary>
      <description>&lt;p&gt;&amp;nbsp;&lt;/p&gt;
</description>
      <guid>133548</guid>
      <pubDate>Sat, 28 Apr 2012 21:16:41 Z</pubDate>
      <itunes:author>Marvin Ray Burns</itunes:author>
      <author>Marvin Ray Burns</author>
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    <item>
      <title>MRB Constant X</title>
      <link>http://www.mapleprimes.com/posts/133236-MRB-Constant-X?ref=Feed:MaplePrimes:Tagged With constants</link>
      <itunes:summary>&lt;p&gt;&amp;nbsp;&lt;/p&gt;
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&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;"&gt;The MRB constant is evaluated by&lt;/span&gt;&lt;/p&gt;
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&lt;td&gt;&lt;/td&gt;&lt;/tr&gt;&lt;/tbody&gt;&lt;/table&gt;&lt;/td&gt;&lt;/tr&gt;&lt;/tbody&gt;&lt;/table&gt;</itunes:summary>
      <description>&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;form name="worksheet_form"&gt;
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&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;"&gt;The MRB constant is evaluated by&lt;/span&gt;&lt;/p&gt;
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      <guid>133236</guid>
      <pubDate>Sat, 21 Apr 2012 18:22:18 Z</pubDate>
      <itunes:author>Marvin Ray Burns</itunes:author>
      <author>Marvin Ray Burns</author>
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    <item>
      <title>MRB constant T</title>
      <link>http://www.mapleprimes.com/posts/129624-MRB-Constant-T?ref=Feed:MaplePrimes:Tagged With constants</link>
      <itunes:summary>&lt;p&gt;&lt;br&gt; &lt;/p&gt;
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&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;"&gt;Let c=MRB constant -1/2&lt;/span&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;/td&gt;&lt;/tr&gt;&lt;/tbody&gt;&lt;/table&gt;</itunes:summary>
      <description>&lt;p&gt;&lt;br&gt; &lt;/p&gt;
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&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;"&gt;Let c=MRB constant -1/2&lt;/span&gt;&lt;/p&gt;
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      <guid>129624</guid>
      <pubDate>Fri, 13 Jan 2012 20:45:19 Z</pubDate>
      <itunes:author>Marvin Ray Burns</itunes:author>
      <author>Marvin Ray Burns</author>
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      <title>MRB constant S part 2</title>
      <link>http://www.mapleprimes.com/posts/129449-MRB-Constant-S-Part-2?ref=Feed:MaplePrimes:Tagged With constants</link>
      <itunes:summary>&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
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&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&amp;nbsp;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/50cb70fc9ee0b48a016934418e45215d.gif" alt="``" width="11" height="23"&gt;&lt;/p&gt;
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&lt;td&gt;&lt;span style="color: #ff0000; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt; &amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
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&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/00313a43d2d41f91d9abdf22b8c1205f.gif" alt="restart; Digits := 64" width="147" height="23"&gt;&lt;/p&gt;
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&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/6ffcfe73e793a50b195577f5a134c3a6.gif" alt="``" width="11" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&amp;nbsp;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/389e5c07f26876f8f4e1e6bd86e6704d.gif" alt="``" width="11" height="23"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/e7f3a86187ab22d73a439f4f2b026775.gif" alt="``" width="11" height="23"&gt;Define s as the following function involving a divergent series.&lt;/p&gt;
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&lt;td&gt;&lt;span style="color: #ff0000; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt; &amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
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&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -16;" src="/view.aspx?sf=129449/428307/108705c6b811d8233bebe120535d6f80.gif" alt="s := proc (x) options operator, arrow; sum((-1)^n*n^(1/n), n = 1 .. x) end proc" width="270" height="42"&gt;&lt;/p&gt;
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&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"&gt;&lt;img style="vertical-align: -20;" src="/view.aspx?sf=129449/428307/47c88b5dab861a7b17820585e7675d78.gif" alt="proc (x) options operator, arrow; sum((-1)^n*n^(1/n), n = 1 .. x) end proc" width="139" height="57"&gt;&lt;/p&gt;
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&lt;td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right"&gt;(1)&lt;/td&gt;
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&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/3e72ac6fe97aa8a369f787ac92ff0547.gif" alt="``" width="11" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/95c190c06ca405ca78b684109abdc5aa.gif" alt="``" width="11" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;span style="color: #ff0000; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt;&amp;nbsp; &lt;/span&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&amp;nbsp;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/8e539167270a8836b239f9f8981145bc.gif" alt="``" width="11" height="23"&gt;The upper limit point of the partial sums, of s is very slowly convergent.&lt;/p&gt;
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&lt;td&gt;&lt;span style="color: #ff0000; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt; &amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
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&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -7;" src="/view.aspx?sf=129449/428307/109f0646a64d79d18eefc5c500ceebaa.gif" alt="evalf(s(100))" width="92" height="24"&gt;&lt;/p&gt;
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&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/ab1b1dcc77a3db10878f7de40ece772a.gif" alt=".211329543346941069485035868216520490712148674852018130412747187" width="489" height="23"&gt;&lt;/p&gt;
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&lt;td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right"&gt;(2)&lt;/td&gt;
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&lt;td&gt;&lt;span style="color: #ff0000; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt; &amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
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&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/f38389dcaa015bb6c52911ba9d0da5a5.gif" alt="evalf(s(1000))" width="103" height="23"&gt;&lt;/p&gt;
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&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/3e1331b710328dd3e47500f61d322ab1.gif" alt=".191323989712141370638688981469071803275457219110707245455878532" width="489" height="23"&gt;&lt;/p&gt;
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&lt;td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right"&gt;(3)&lt;/td&gt;
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&lt;td&gt;&lt;span style="color: #ff0000; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt; &amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
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&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/d06f95ee7f0178207ff6d163d52044f4.gif" alt="evalf(s(10000))" width="107" height="23"&gt;&lt;/p&gt;
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&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/2c4adfa512e8254767bddcabb6dde52f.gif" alt=".188320351076950504638897789942367214051161086517598649780487746" width="489" height="23"&gt;&lt;/p&gt;
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&lt;td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right"&gt;(4)&lt;/td&gt;
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&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;"&gt;&amp;nbsp; &lt;/span&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/d586c488c66f6f3c41ec8825b2d4fc49.gif" alt="``" width="11" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;"&gt;Let mrb be tthe upper limit point of s as x goes to infinity.&lt;/span&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/ffb51a9872dd12cfec236e7658ebc7e4.gif" alt="``" width="11" height="23"&gt;&lt;/p&gt;
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&lt;td&gt;&lt;span style="color: #ff0000; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt; &amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
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&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/fe31c3d021666b1e420f275b0ca7c29c.gif" alt="mrb := evalf(sum((-1)^n*(n^(1/n)-1), n = 1 .. infinity))" width="378" height="23"&gt;&lt;/p&gt;
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&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/d05ee7120b3a8adbc8b8f300f481152e.gif" alt=".1878596424620671202485179340542732300559030949001387861720046841" width="541" height="23"&gt;&lt;/p&gt;
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&lt;td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right"&gt;(5)&lt;/td&gt;
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&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/a38d3c7490f9a390ae4169552e7f906e.gif" alt="``" width="11" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/c67bdedf9025ebc68841369319a16e51.gif" alt="``" width="11" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/445c4222dbb87fdb51a363509a59e35d.gif" alt="``" width="11" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;span style="color: #ff0000; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt;&amp;nbsp; &lt;/span&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;"&gt;Define f as the following function involving the divergnet series &lt;/span&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/762101ecadef6ddeea2eba3540f1a220.gif" alt="sum((-1)^n*(n^(a/n)-a), n = 1 .. infinity)." width="277" height="23"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/fc6746a7cd2779410a6d310dffff882d.gif" alt="NULL" width="11" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/8380b2582e667a30f6644b5908befdc1.gif" alt="``" width="11" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/f9155d4b2e720a98ebd310a4bc1784e9.gif" alt="``" width="11" height="23"&gt;&lt;/p&gt;
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&lt;td&gt;&lt;span style="color: #ff0000; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt; &amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/9f16c9388d842d00d87b6bf7f4847fa7.gif" alt="f := proc (a) options operator, arrow; sum((-1)^n*(n^(a/n)-a), n = 1 .. infinity) end proc" width="329" height="23"&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;
&lt;table&gt;
&lt;tbody&gt;
&lt;tr valign="baseline"&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"&gt;&lt;img style="vertical-align: -20;" src="/view.aspx?sf=129449/428307/e84f05574e8833da5342ed702342f031.gif" alt="proc (a) options operator, arrow; sum((-1)^n*(n^(a/n)-a), n = 1 .. infinity) end proc" width="185" height="56"&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right"&gt;(6)&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/c576e936c552a33942a07746cb9c95b5.gif" alt="``" width="11" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/1fbf7647774fd8973c5224b94f36639f.gif" alt="``" width="11" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;span style="color: #ff0000; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt;&amp;nbsp; &lt;/span&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&amp;nbsp;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/c8610f9c72a1e30e85543b1d6e81123e.gif" alt="``" width="11" height="23"&gt;Let c be the value for a in the neighborhood of 26 such that f(a)=mrb.&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/684bd4c9dc63624cb064b06a88280aff.gif" alt="c := fsolve(eval(f(x)) = mrb, x = 26)" width="239" height="23"&gt;&lt;/p&gt;
&lt;table&gt;
&lt;tbody&gt;
&lt;tr valign="baseline"&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/1bd740337254b56fcd1fec3d522b690f.gif" alt="25.71864739101744668471488151161460875040712539231550975094037406" width="489" height="23"&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right"&gt;(7)&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/35a37230476460513067ccaa88ac0864.gif" alt="``" width="11" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/eda202359a41c4dd905ec4a04e5d235b.gif" alt="``" width="11" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&amp;nbsp;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/3e880430e216c2c152fd4e7b705e9ee3.gif" alt="``" width="11" height="23"&gt;The average of the upper and lower limit points of the partil sums of f converges much faster than the &amp;nbsp;upper limit point of the partial sums of s.&lt;/p&gt;
&lt;table style="margin-left: 0px; margin-right: 0px;"&gt;
&lt;tbody&gt;
&lt;tr valign="baseline"&gt;
&lt;td&gt;&lt;span style="color: #ff0000; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt; &amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -52;" src="/view.aspx?sf=129449/428307/af34d3b8c84ef90929ab7304ea6cee20.gif" alt="evalf((sum((-1)^n*(n^(c/n)-c), n = 1 .. 100)+sum((-1)^n*(n^(c/n)-c), n = 1 .. 101))*(1/2))" width="576" height="78" align="middle"&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;
&lt;table&gt;
&lt;tbody&gt;
&lt;tr valign="baseline"&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/af8985b67df1e6a2df1b170ca841431f.gif" alt=".195238896203546569611605945649919224928195587923897718988014700" width="489" height="23"&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right"&gt;(8)&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;
&lt;table style="margin-left: 0px; margin-right: 0px;"&gt;
&lt;tbody&gt;
&lt;tr valign="baseline"&gt;
&lt;td&gt;&lt;span style="color: #ff0000; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt; &amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -52;" src="/view.aspx?sf=129449/428307/8f824790246a79671e9cfc065d7ea639.gif" alt="evalf((sum((-1)^n*(n^(c/n)-c), n = 1 .. 1000)+sum((-1)^n*(n^(c/n)-c), n = 1 .. 1001))*(1/2))" width="576" height="78" align="middle"&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;
&lt;table&gt;
&lt;tbody&gt;
&lt;tr valign="baseline"&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/670f1f27366a9546fe6345f8e5883809.gif" alt=".187904922391719396683391551158554482265830937732923110694243700" width="489" height="23"&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right"&gt;(9)&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;
&lt;table style="margin-left: 0px; margin-right: 0px;"&gt;
&lt;tbody&gt;
&lt;tr valign="baseline"&gt;
&lt;td&gt;&lt;span style="color: #ff0000; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt; &amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -52;" src="/view.aspx?sf=129449/428307/df912ba8d8f60830bbaa82dbb3c878ef.gif" alt="evalf((sum((-1)^n*(n^(c/n)-c), n = 1 .. 10000)+sum((-1)^n*(n^(c/n)-c), n = 1 .. 10001))*(1/2))" width="576" height="78" align="middle"&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;
&lt;table&gt;
&lt;tbody&gt;
&lt;tr valign="baseline"&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/b5ad4c55680b644f89b8c886d26f07b4.gif" alt=".187860182910509428926222275077446745338505139578191116998518780" width="489" height="23"&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right"&gt;(10)&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;
&lt;span style="font-size: small;"&gt;&lt;br&gt;&lt;/span&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;
&lt;input type="hidden" name="sequence" value="1"&gt; &lt;input type="hidden" name="cmd" value="none"&gt;&lt;/form&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;&lt;a href="/view.aspx?sf=129449/428307/Jan72012.mw"&gt;Download Jan72012.mw&lt;/a&gt;&lt;/p&gt;
</itunes:summary>
      <description>&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;form name="worksheet_form"&gt;
&lt;table style="width: 576px;" align="center"&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&amp;nbsp;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/50cb70fc9ee0b48a016934418e45215d.gif" alt="``" width="11" height="23"&gt;&lt;/p&gt;
&lt;table style="margin-left: 0px; margin-right: 0px;"&gt;
&lt;tbody&gt;
&lt;tr valign="baseline"&gt;
&lt;td&gt;&lt;span style="color: #ff0000; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt; &amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/00313a43d2d41f91d9abdf22b8c1205f.gif" alt="restart; Digits := 64" width="147" height="23"&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/6ffcfe73e793a50b195577f5a134c3a6.gif" alt="``" width="11" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&amp;nbsp;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/389e5c07f26876f8f4e1e6bd86e6704d.gif" alt="``" width="11" height="23"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/e7f3a86187ab22d73a439f4f2b026775.gif" alt="``" width="11" height="23"&gt;Define s as the following function involving a divergent series.&lt;/p&gt;
&lt;table style="margin-left: 0px; margin-right: 0px;"&gt;
&lt;tbody&gt;
&lt;tr valign="baseline"&gt;
&lt;td&gt;&lt;span style="color: #ff0000; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt; &amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -16;" src="/view.aspx?sf=129449/428307/108705c6b811d8233bebe120535d6f80.gif" alt="s := proc (x) options operator, arrow; sum((-1)^n*n^(1/n), n = 1 .. x) end proc" width="270" height="42"&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;
&lt;table&gt;
&lt;tbody&gt;
&lt;tr valign="baseline"&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"&gt;&lt;img style="vertical-align: -20;" src="/view.aspx?sf=129449/428307/47c88b5dab861a7b17820585e7675d78.gif" alt="proc (x) options operator, arrow; sum((-1)^n*n^(1/n), n = 1 .. x) end proc" width="139" height="57"&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right"&gt;(1)&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/3e72ac6fe97aa8a369f787ac92ff0547.gif" alt="``" width="11" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/95c190c06ca405ca78b684109abdc5aa.gif" alt="``" width="11" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;span style="color: #ff0000; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt;&amp;nbsp; &lt;/span&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&amp;nbsp;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/8e539167270a8836b239f9f8981145bc.gif" alt="``" width="11" height="23"&gt;The upper limit point of the partial sums, of s is very slowly convergent.&lt;/p&gt;
&lt;table style="margin-left: 0px; margin-right: 0px;"&gt;
&lt;tbody&gt;
&lt;tr valign="baseline"&gt;
&lt;td&gt;&lt;span style="color: #ff0000; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt; &amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -7;" src="/view.aspx?sf=129449/428307/109f0646a64d79d18eefc5c500ceebaa.gif" alt="evalf(s(100))" width="92" height="24"&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;
&lt;table&gt;
&lt;tbody&gt;
&lt;tr valign="baseline"&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/ab1b1dcc77a3db10878f7de40ece772a.gif" alt=".211329543346941069485035868216520490712148674852018130412747187" width="489" height="23"&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right"&gt;(2)&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;
&lt;table style="margin-left: 0px; margin-right: 0px;"&gt;
&lt;tbody&gt;
&lt;tr valign="baseline"&gt;
&lt;td&gt;&lt;span style="color: #ff0000; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt; &amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/f38389dcaa015bb6c52911ba9d0da5a5.gif" alt="evalf(s(1000))" width="103" height="23"&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;
&lt;table&gt;
&lt;tbody&gt;
&lt;tr valign="baseline"&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/3e1331b710328dd3e47500f61d322ab1.gif" alt=".191323989712141370638688981469071803275457219110707245455878532" width="489" height="23"&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right"&gt;(3)&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;
&lt;table style="margin-left: 0px; margin-right: 0px;"&gt;
&lt;tbody&gt;
&lt;tr valign="baseline"&gt;
&lt;td&gt;&lt;span style="color: #ff0000; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt; &amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/d06f95ee7f0178207ff6d163d52044f4.gif" alt="evalf(s(10000))" width="107" height="23"&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;
&lt;table&gt;
&lt;tbody&gt;
&lt;tr valign="baseline"&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/2c4adfa512e8254767bddcabb6dde52f.gif" alt=".188320351076950504638897789942367214051161086517598649780487746" width="489" height="23"&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right"&gt;(4)&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;"&gt;&amp;nbsp; &lt;/span&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/d586c488c66f6f3c41ec8825b2d4fc49.gif" alt="``" width="11" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;"&gt;Let mrb be tthe upper limit point of s as x goes to infinity.&lt;/span&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/ffb51a9872dd12cfec236e7658ebc7e4.gif" alt="``" width="11" height="23"&gt;&lt;/p&gt;
&lt;table style="margin-left: 0px; margin-right: 0px;"&gt;
&lt;tbody&gt;
&lt;tr valign="baseline"&gt;
&lt;td&gt;&lt;span style="color: #ff0000; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt; &amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/fe31c3d021666b1e420f275b0ca7c29c.gif" alt="mrb := evalf(sum((-1)^n*(n^(1/n)-1), n = 1 .. infinity))" width="378" height="23"&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;
&lt;table&gt;
&lt;tbody&gt;
&lt;tr valign="baseline"&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/d05ee7120b3a8adbc8b8f300f481152e.gif" alt=".1878596424620671202485179340542732300559030949001387861720046841" width="541" height="23"&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right"&gt;(5)&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/a38d3c7490f9a390ae4169552e7f906e.gif" alt="``" width="11" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/c67bdedf9025ebc68841369319a16e51.gif" alt="``" width="11" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/445c4222dbb87fdb51a363509a59e35d.gif" alt="``" width="11" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;span style="color: #ff0000; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt;&amp;nbsp; &lt;/span&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;"&gt;Define f as the following function involving the divergnet series &lt;/span&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/762101ecadef6ddeea2eba3540f1a220.gif" alt="sum((-1)^n*(n^(a/n)-a), n = 1 .. infinity)." width="277" height="23"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/fc6746a7cd2779410a6d310dffff882d.gif" alt="NULL" width="11" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/8380b2582e667a30f6644b5908befdc1.gif" alt="``" width="11" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/f9155d4b2e720a98ebd310a4bc1784e9.gif" alt="``" width="11" height="23"&gt;&lt;/p&gt;
&lt;table style="margin-left: 0px; margin-right: 0px;"&gt;
&lt;tbody&gt;
&lt;tr valign="baseline"&gt;
&lt;td&gt;&lt;span style="color: #ff0000; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt; &amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/9f16c9388d842d00d87b6bf7f4847fa7.gif" alt="f := proc (a) options operator, arrow; sum((-1)^n*(n^(a/n)-a), n = 1 .. infinity) end proc" width="329" height="23"&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;
&lt;table&gt;
&lt;tbody&gt;
&lt;tr valign="baseline"&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"&gt;&lt;img style="vertical-align: -20;" src="/view.aspx?sf=129449/428307/e84f05574e8833da5342ed702342f031.gif" alt="proc (a) options operator, arrow; sum((-1)^n*(n^(a/n)-a), n = 1 .. infinity) end proc" width="185" height="56"&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right"&gt;(6)&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/c576e936c552a33942a07746cb9c95b5.gif" alt="``" width="11" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/1fbf7647774fd8973c5224b94f36639f.gif" alt="``" width="11" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;span style="color: #ff0000; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt;&amp;nbsp; &lt;/span&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&amp;nbsp;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/c8610f9c72a1e30e85543b1d6e81123e.gif" alt="``" width="11" height="23"&gt;Let c be the value for a in the neighborhood of 26 such that f(a)=mrb.&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/684bd4c9dc63624cb064b06a88280aff.gif" alt="c := fsolve(eval(f(x)) = mrb, x = 26)" width="239" height="23"&gt;&lt;/p&gt;
&lt;table&gt;
&lt;tbody&gt;
&lt;tr valign="baseline"&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/1bd740337254b56fcd1fec3d522b690f.gif" alt="25.71864739101744668471488151161460875040712539231550975094037406" width="489" height="23"&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right"&gt;(7)&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/35a37230476460513067ccaa88ac0864.gif" alt="``" width="11" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/eda202359a41c4dd905ec4a04e5d235b.gif" alt="``" width="11" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&amp;nbsp;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/3e880430e216c2c152fd4e7b705e9ee3.gif" alt="``" width="11" height="23"&gt;The average of the upper and lower limit points of the partil sums of f converges much faster than the &amp;nbsp;upper limit point of the partial sums of s.&lt;/p&gt;
&lt;table style="margin-left: 0px; margin-right: 0px;"&gt;
&lt;tbody&gt;
&lt;tr valign="baseline"&gt;
&lt;td&gt;&lt;span style="color: #ff0000; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt; &amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -52;" src="/view.aspx?sf=129449/428307/af34d3b8c84ef90929ab7304ea6cee20.gif" alt="evalf((sum((-1)^n*(n^(c/n)-c), n = 1 .. 100)+sum((-1)^n*(n^(c/n)-c), n = 1 .. 101))*(1/2))" width="576" height="78" align="middle"&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;
&lt;table&gt;
&lt;tbody&gt;
&lt;tr valign="baseline"&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/af8985b67df1e6a2df1b170ca841431f.gif" alt=".195238896203546569611605945649919224928195587923897718988014700" width="489" height="23"&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right"&gt;(8)&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;
&lt;table style="margin-left: 0px; margin-right: 0px;"&gt;
&lt;tbody&gt;
&lt;tr valign="baseline"&gt;
&lt;td&gt;&lt;span style="color: #ff0000; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt; &amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -52;" src="/view.aspx?sf=129449/428307/8f824790246a79671e9cfc065d7ea639.gif" alt="evalf((sum((-1)^n*(n^(c/n)-c), n = 1 .. 1000)+sum((-1)^n*(n^(c/n)-c), n = 1 .. 1001))*(1/2))" width="576" height="78" align="middle"&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;
&lt;table&gt;
&lt;tbody&gt;
&lt;tr valign="baseline"&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/670f1f27366a9546fe6345f8e5883809.gif" alt=".187904922391719396683391551158554482265830937732923110694243700" width="489" height="23"&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right"&gt;(9)&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;
&lt;table style="margin-left: 0px; margin-right: 0px;"&gt;
&lt;tbody&gt;
&lt;tr valign="baseline"&gt;
&lt;td&gt;&lt;span style="color: #ff0000; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt; &amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -52;" src="/view.aspx?sf=129449/428307/df912ba8d8f60830bbaa82dbb3c878ef.gif" alt="evalf((sum((-1)^n*(n^(c/n)-c), n = 1 .. 10000)+sum((-1)^n*(n^(c/n)-c), n = 1 .. 10001))*(1/2))" width="576" height="78" align="middle"&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;
&lt;table&gt;
&lt;tbody&gt;
&lt;tr valign="baseline"&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129449/428307/b5ad4c55680b644f89b8c886d26f07b4.gif" alt=".187860182910509428926222275077446745338505139578191116998518780" width="489" height="23"&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right"&gt;(10)&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;
&lt;span style="font-size: small;"&gt;&lt;br&gt;&lt;/span&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;
&lt;input type="hidden" name="sequence" value="1"&gt; &lt;input type="hidden" name="cmd" value="none"&gt;&lt;/form&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;&lt;a href="/view.aspx?sf=129449/428307/Jan72012.mw"&gt;Download Jan72012.mw&lt;/a&gt;&lt;/p&gt;
</description>
      <guid>129449</guid>
      <pubDate>Sun, 08 Jan 2012 03:45:16 Z</pubDate>
      <itunes:author>Marvin Ray Burns</itunes:author>
      <author>Marvin Ray Burns</author>
    </item>
    <item>
      <title>MRB constant S</title>
      <link>http://www.mapleprimes.com/posts/129276-MRB-Constant-S?ref=Feed:MaplePrimes:Tagged With constants</link>
      <itunes:summary>&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;&lt;br&gt; &lt;/p&gt;
&lt;form name="worksheet_form"&gt;
&lt;table style="width: 576px;" align="center"&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/ViewTemp.ashx?f=19142_1325520050/ebbb6e13f5db79fa040a3ea27601fe30.gif" alt="NULL" width="11" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/ViewTemp.ashx?f=19142_1325520050/9d2f03b14dd77007a47c5777b45a8e98.gif" alt="NULL" width="11" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;"&gt;Let f(c)= &lt;/span&gt;&lt;img style="vertical-align: -20;" src="/ViewTemp.ashx?f=19142_1325520050/6ec22760d9e472f66115e5fb292472c3.gif" alt="sum((-1)^n*(n^(c/n)-c), n = 1 .. infinity)" width="160" height="55"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/ViewTemp.ashx?f=19142_1325520050/a657bd3f5f0d13766ca6688298dd17f8.gif" alt="NULL" width="11" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/ViewTemp.ashx?f=19142_1325520050/d76630c251ed7e0c6ecd9d69591427f2.gif" alt="NULL" width="11" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;"&gt;Then f(1) = the MRB constant:&lt;/span&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -20;" src="/ViewTemp.ashx?f=19142_1325520050/acc809b32be053d4d8d1c11a4082c719.gif" alt="evalf(eval(sum((-1)^n*(n^(c/n)-c), n = 1 .. infinity), c = 1))" width="289" height="55"&gt;&lt;span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;"&gt;&amp;nbsp;= &lt;/span&gt;&lt;img style="vertical-align: -6;" src="/ViewTemp.ashx?f=19142_1325520050/16d1a5f685766a3d0942dc26d458c776.gif" alt=".1878596425" width="92" height="23"&gt;&lt;img style="vertical-align: -6;" src="/ViewTemp.ashx?f=19142_1325520050/86e3c8190d8788152f1bda3bb04b281a.gif" alt="NULL" width="11" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/ViewTemp.ashx?f=19142_1325520050/68fda2bf31672f1bf37e67fe4627e693.gif" alt="NULL" width="11" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/ViewTemp.ashx?f=19142_1325520050/8ba3baaf08fa9ba57ec9299842a8ee4e.gif" alt="NULL" width="11" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;"&gt;What if we change the value of c and use Levin's u-transform to compute the values for the analytic extension of the sum?&lt;/span&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;"&gt;Then can we find values for c such that f(c)=c?&lt;/span&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;"&gt;&amp;nbsp; &lt;/span&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -20;" src="/ViewTemp.ashx?f=19142_1325520050/06599019c83584d59ef1a581f06c4abc.gif" alt="evalf(eval(sum((-1)^n*(n^(c/n)-c), n = 1 .. infinity), c = -1.351776595077954))" width="411" height="55"&gt;&lt;span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;"&gt;&amp;nbsp;= &lt;/span&gt;&lt;img style="vertical-align: -6;" src="/ViewTemp.ashx?f=19142_1325520050/6c9e1458306217ab372908a3f909cd60.gif" alt="-1.351776595" width="94" height="23"&gt;&lt;span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;"&gt;&amp;nbsp; &lt;/span&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -20;" src="/ViewTemp.ashx?f=19142_1325520050/148080fa89185a88d1746764f4b6ad17.gif" alt="evalf(eval(sum((-1)^n*(n^(c/n)-c), n = 1 .. infinity), c = 7.020400867228059))" width="405" height="55"&gt;&lt;span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;"&gt;&amp;nbsp;= &lt;/span&gt;&lt;img style="vertical-align: -6;" src="/ViewTemp.ashx?f=19142_1325520050/da4e05774729cc2b6e4699dd729e00eb.gif" alt="7.020400867" width="84" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -20;" src="/ViewTemp.ashx?f=19142_1325520050/26b4d57117db6fc322156027ee9cccd1.gif" alt="evalf(eval(sum((-1)^n*(n^(c/n)-c), n = 1 .. infinity), c = 25.58774196597964))" width="405" height="55"&gt;&lt;span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;"&gt;&amp;nbsp;= &lt;/span&gt;&lt;img style="vertical-align: -6;" src="/ViewTemp.ashx?f=19142_1325520050/f9fc770880c018e2133f9efb14a5f42e.gif" alt="25.58880851" width="84" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/ViewTemp.ashx?f=19142_1325520050/f5b87516b8060d8fcd2c81e21bc7dfeb.gif" alt="``" width="11" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;"&gt;As an alalytic extension of the sum is there another value for c such that f(c) = the MRB constant? I haven't found one.&lt;/span&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/ViewTemp.ashx?f=19142_1325520050/1e5e11f657d98a0c8bf1b97b764b89b9.gif" alt="NULL" width="11" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;"&gt;&amp;nbsp; &lt;/span&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;"&gt;&amp;nbsp; &lt;/span&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/ViewTemp.ashx?f=19142_1325520050/a09bc2b1af29d38723ef0b8c790525d2.gif" alt="``" width="11" height="23"&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;
&lt;input type="hidden" name="sequence" value="1"&gt; &lt;input type="hidden" name="cmd" value="none"&gt;&lt;/form&gt;
&lt;p&gt;&lt;br&gt; &lt;/p&gt;
&lt;p&gt;&lt;a href="/ViewTemp.ashx?f=19142_1325520050/jan022012.mw"&gt;Download jan022012.mw&lt;/a&gt;&lt;/p&gt;
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</itunes:summary>
      <description>&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;&lt;br&gt; &lt;/p&gt;
&lt;form name="worksheet_form"&gt;
&lt;table style="width: 576px;" align="center"&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/ViewTemp.ashx?f=19142_1325520050/ebbb6e13f5db79fa040a3ea27601fe30.gif" alt="NULL" width="11" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/ViewTemp.ashx?f=19142_1325520050/9d2f03b14dd77007a47c5777b45a8e98.gif" alt="NULL" width="11" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;"&gt;Let f(c)= &lt;/span&gt;&lt;img style="vertical-align: -20;" src="/ViewTemp.ashx?f=19142_1325520050/6ec22760d9e472f66115e5fb292472c3.gif" alt="sum((-1)^n*(n^(c/n)-c), n = 1 .. infinity)" width="160" height="55"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/ViewTemp.ashx?f=19142_1325520050/a657bd3f5f0d13766ca6688298dd17f8.gif" alt="NULL" width="11" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/ViewTemp.ashx?f=19142_1325520050/d76630c251ed7e0c6ecd9d69591427f2.gif" alt="NULL" width="11" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;"&gt;Then f(1) = the MRB constant:&lt;/span&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -20;" src="/ViewTemp.ashx?f=19142_1325520050/acc809b32be053d4d8d1c11a4082c719.gif" alt="evalf(eval(sum((-1)^n*(n^(c/n)-c), n = 1 .. infinity), c = 1))" width="289" height="55"&gt;&lt;span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;"&gt;&amp;nbsp;= &lt;/span&gt;&lt;img style="vertical-align: -6;" src="/ViewTemp.ashx?f=19142_1325520050/16d1a5f685766a3d0942dc26d458c776.gif" alt=".1878596425" width="92" height="23"&gt;&lt;img style="vertical-align: -6;" src="/ViewTemp.ashx?f=19142_1325520050/86e3c8190d8788152f1bda3bb04b281a.gif" alt="NULL" width="11" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/ViewTemp.ashx?f=19142_1325520050/68fda2bf31672f1bf37e67fe4627e693.gif" alt="NULL" width="11" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/ViewTemp.ashx?f=19142_1325520050/8ba3baaf08fa9ba57ec9299842a8ee4e.gif" alt="NULL" width="11" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;"&gt;What if we change the value of c and use Levin's u-transform to compute the values for the analytic extension of the sum?&lt;/span&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;"&gt;Then can we find values for c such that f(c)=c?&lt;/span&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;"&gt;&amp;nbsp; &lt;/span&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -20;" src="/ViewTemp.ashx?f=19142_1325520050/06599019c83584d59ef1a581f06c4abc.gif" alt="evalf(eval(sum((-1)^n*(n^(c/n)-c), n = 1 .. infinity), c = -1.351776595077954))" width="411" height="55"&gt;&lt;span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;"&gt;&amp;nbsp;= &lt;/span&gt;&lt;img style="vertical-align: -6;" src="/ViewTemp.ashx?f=19142_1325520050/6c9e1458306217ab372908a3f909cd60.gif" alt="-1.351776595" width="94" height="23"&gt;&lt;span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;"&gt;&amp;nbsp; &lt;/span&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -20;" src="/ViewTemp.ashx?f=19142_1325520050/148080fa89185a88d1746764f4b6ad17.gif" alt="evalf(eval(sum((-1)^n*(n^(c/n)-c), n = 1 .. infinity), c = 7.020400867228059))" width="405" height="55"&gt;&lt;span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;"&gt;&amp;nbsp;= &lt;/span&gt;&lt;img style="vertical-align: -6;" src="/ViewTemp.ashx?f=19142_1325520050/da4e05774729cc2b6e4699dd729e00eb.gif" alt="7.020400867" width="84" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -20;" src="/ViewTemp.ashx?f=19142_1325520050/26b4d57117db6fc322156027ee9cccd1.gif" alt="evalf(eval(sum((-1)^n*(n^(c/n)-c), n = 1 .. infinity), c = 25.58774196597964))" width="405" height="55"&gt;&lt;span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;"&gt;&amp;nbsp;= &lt;/span&gt;&lt;img style="vertical-align: -6;" src="/ViewTemp.ashx?f=19142_1325520050/f9fc770880c018e2133f9efb14a5f42e.gif" alt="25.58880851" width="84" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/ViewTemp.ashx?f=19142_1325520050/f5b87516b8060d8fcd2c81e21bc7dfeb.gif" alt="``" width="11" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;"&gt;As an alalytic extension of the sum is there another value for c such that f(c) = the MRB constant? I haven't found one.&lt;/span&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/ViewTemp.ashx?f=19142_1325520050/1e5e11f657d98a0c8bf1b97b764b89b9.gif" alt="NULL" width="11" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;"&gt;&amp;nbsp; &lt;/span&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;"&gt;&amp;nbsp; &lt;/span&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/ViewTemp.ashx?f=19142_1325520050/a09bc2b1af29d38723ef0b8c790525d2.gif" alt="``" width="11" height="23"&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;
&lt;input type="hidden" name="sequence" value="1"&gt; &lt;input type="hidden" name="cmd" value="none"&gt;&lt;/form&gt;
&lt;p&gt;&lt;br&gt; &lt;/p&gt;
&lt;p&gt;&lt;a href="/ViewTemp.ashx?f=19142_1325520050/jan022012.mw"&gt;Download jan022012.mw&lt;/a&gt;&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
</description>
      <guid>129276</guid>
      <pubDate>Mon, 02 Jan 2012 16:05:36 Z</pubDate>
      <itunes:author>Marvin Ray Burns</itunes:author>
      <author>Marvin Ray Burns</author>
    </item>
    <item>
      <title>MRB constant R</title>
      <link>http://www.mapleprimes.com/posts/129265-MRB-Constant-R?ref=Feed:MaplePrimes:Tagged With constants</link>
      <itunes:summary>&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;form style="text-align: -webkit-left;" name="worksheet_form"&gt;&lt;/form&gt;&lt;form name="worksheet_form"&gt;
&lt;table style="width: 576px;" align="center"&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129265/427974/3c88004de20579b971db37cd7355cfb0.gif" alt="``" width="11" height="23"&gt;&lt;/p&gt;
&lt;/td&gt;&lt;/tr&gt;&lt;/tbody&gt;&lt;/table&gt;</itunes:summary>
      <description>&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;form style="text-align: -webkit-left;" name="worksheet_form"&gt;&lt;/form&gt;&lt;form name="worksheet_form"&gt;
&lt;table style="width: 576px;" align="center"&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=129265/427974/3c88004de20579b971db37cd7355cfb0.gif" alt="``" width="11" height="23"&gt;&lt;/p&gt;
&lt;/td&gt;&lt;/tr&gt;&lt;/tbody&gt;&lt;/table&gt;</description>
      <guid>129265</guid>
      <pubDate>Sun, 01 Jan 2012 19:42:52 Z</pubDate>
      <itunes:author>Marvin Ray Burns</itunes:author>
      <author>Marvin Ray Burns</author>
    </item>
    <item>
      <title>MRB constant P</title>
      <link>http://www.mapleprimes.com/posts/125427-MRB-Constant-P?ref=Feed:MaplePrimes:Tagged With constants</link>
      <itunes:summary>&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;The MRB constant = &amp;nbsp; &amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=cafdd43c441db14587d65c43a8fc2e77.gif" alt="sum((-1)^n*(n^(1/n)-1), n = 1 .. infinity)"&gt;&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;Concerning the following divergent and convergent series, we see that&lt;/p&gt;
&lt;p&gt;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=053bcd8e46653069739f6484211ca240.gif" alt="sum((-1)^n*(n^(1/n)-x), n = 1 .. infinity)"&gt;=</itunes:summary>
      <description>&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;The MRB constant = &amp;nbsp; &amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=cafdd43c441db14587d65c43a8fc2e77.gif" alt="sum((-1)^n*(n^(1/n)-1), n = 1 .. infinity)"&gt;&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;Concerning the following divergent and convergent series, we see that&lt;/p&gt;
&lt;p&gt;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=053bcd8e46653069739f6484211ca240.gif" alt="sum((-1)^n*(n^(1/n)-x), n = 1 .. infinity)"&gt;=</description>
      <guid>125427</guid>
      <pubDate>Sun, 04 Sep 2011 22:43:46 Z</pubDate>
      <itunes:author>Marvin Ray Burns</itunes:author>
      <author>Marvin Ray Burns</author>
    </item>
    <item>
      <title>Maple 15.02 -- when?</title>
      <link>http://www.mapleprimes.com/questions/124775-Maple-1502--When?ref=Feed:MaplePrimes:Tagged With constants</link>
      <itunes:summary>&lt;p&gt;When can we expect Maple 15.02 to appear, to correct that major error of matrix multiplication and the plotting problem with the classic interface in particular?&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; Now a new set of fundamental physical constants has been released, as of 2011 June, making the values embedded in Maple's package Scientific Constants from the preceding millennium a further step obsolescent.&amp;nbsp; I understand, however, that the values of mathematical constants pi and exp(1) are still current.</itunes:summary>
      <description>&lt;p&gt;When can we expect Maple 15.02 to appear, to correct that major error of matrix multiplication and the plotting problem with the classic interface in particular?&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; Now a new set of fundamental physical constants has been released, as of 2011 June, making the values embedded in Maple's package Scientific Constants from the preceding millennium a further step obsolescent.&amp;nbsp; I understand, however, that the values of mathematical constants pi and exp(1) are still current.</description>
      <guid>124775</guid>
      <pubDate>Tue, 16 Aug 2011 12:30:00 Z</pubDate>
      <itunes:author>J F Ogilvie</itunes:author>
      <author>J F Ogilvie</author>
    </item>
    <item>
      <title>fourier coefficients</title>
      <link>http://www.mapleprimes.com/questions/124597-Fourier-Coefficients?ref=Feed:MaplePrimes:Tagged With constants</link>
      <itunes:summary>&lt;p&gt;HI,&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;I am trying to solve for fourier coefficients but can't figure out the error in the code. Need help to debug the code.&lt;/p&gt;
&lt;p&gt;Also if possible how to find the harmonics in the curve defined in the code.&lt;/p&gt;
&lt;p&gt;following is the website from where i got this code&lt;/p&gt;
&lt;p&gt;http://www.mapleprimes.com/questions/121551-Fourier-Serie-And-Discrete-Fourier-Transform&lt;/p&gt;
&lt;p&gt;&lt;a href="/ViewTemp.ashx?f=142352_1313061065/fouriercoefficient_h.mw"&gt;fouriercoefficient_h.mw&lt;/a&gt;</itunes:summary>
      <description>&lt;p&gt;HI,&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;I am trying to solve for fourier coefficients but can't figure out the error in the code. Need help to debug the code.&lt;/p&gt;
&lt;p&gt;Also if possible how to find the harmonics in the curve defined in the code.&lt;/p&gt;
&lt;p&gt;following is the website from where i got this code&lt;/p&gt;
&lt;p&gt;http://www.mapleprimes.com/questions/121551-Fourier-Serie-And-Discrete-Fourier-Transform&lt;/p&gt;
&lt;p&gt;&lt;a href="/ViewTemp.ashx?f=142352_1313061065/fouriercoefficient_h.mw"&gt;fouriercoefficient_h.mw&lt;/a&gt;</description>
      <guid>124597</guid>
      <pubDate>Thu, 11 Aug 2011 11:23:56 Z</pubDate>
      <itunes:author>AliKhan</itunes:author>
      <author>AliKhan</author>
    </item>
    <item>
      <title>Maple 15 Sets a World Record for the Computation of a Constant You’ve Probably Never Heard Of</title>
      <link>http://www.mapleprimes.com/maplesoftblog/123419-Maple-15-Sets-A-World-Record-For-The?ref=Feed:MaplePrimes:Tagged With constants</link>
      <itunes:summary>&lt;p style="margin: 0 0 0 0; padding-top: 8px; padding-bottom: 2px;" align="left"&gt;&lt;span style="color: #000000; font-size: 133%; font-weight: bold; font-style: normal;"&gt;The problem&lt;/span&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;span style="color: #000000; font-size: 100%; font-weight: normal; font-style: normal;"&gt;Back in 1996 I was working for the Symbolic Computation Group at the University of Waterloo, developing algorithms and code...&lt;/span&gt;</itunes:summary>
      <description>&lt;p style="margin: 0 0 0 0; padding-top: 8px; padding-bottom: 2px;" align="left"&gt;&lt;span style="color: #000000; font-size: 133%; font-weight: bold; font-style: normal;"&gt;The problem&lt;/span&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;span style="color: #000000; font-size: 100%; font-weight: normal; font-style: normal;"&gt;Back in 1996 I was working for the Symbolic Computation Group at the University of Waterloo, developing algorithms and code...&lt;/span&gt;</description>
      <guid>123419</guid>
      <pubDate>Wed, 29 Jun 2011 18:26:39 Z</pubDate>
      <itunes:author>Dave Hare</itunes:author>
      <author>Dave Hare</author>
    </item>
    <item>
      <title>Convergents Constants</title>
      <link>http://www.mapleprimes.com/posts/120664-Convergents-Constants?ref=Feed:MaplePrimes:Tagged With constants</link>
      <itunes:summary>&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;Here is the progress made in the investigation of what I call the convergents constants:&lt;br&gt;&lt;a href="https://oeis.org/wiki/Table_of_convergents_constants"&gt;https://oeis.org/wiki/Table_of_convergents_constants&lt;br&gt;&lt;/a&gt;&lt;/p&gt;
&lt;p&gt;I wonder if anyone would be interested in adding anything to it. I would like to see the convergents constants studied some&amp;nbsp;in Maple to compare with my Mathematica results; my investigation is in dire need of some proof other than my...</itunes:summary>
      <description>&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;Here is the progress made in the investigation of what I call the convergents constants:&lt;br&gt;&lt;a href="https://oeis.org/wiki/Table_of_convergents_constants"&gt;https://oeis.org/wiki/Table_of_convergents_constants&lt;br&gt;&lt;/a&gt;&lt;/p&gt;
&lt;p&gt;I wonder if anyone would be interested in adding anything to it. I would like to see the convergents constants studied some&amp;nbsp;in Maple to compare with my Mathematica results; my investigation is in dire need of some proof other than my...</description>
      <guid>120664</guid>
      <pubDate>Mon, 30 May 2011 04:30:11 Z</pubDate>
      <itunes:author>Marvin Ray Burns</itunes:author>
      <author>Marvin Ray Burns</author>
    </item>
    <item>
      <title>Solving ODE system</title>
      <link>http://www.mapleprimes.com/questions/103336-Solving-ODE-System?ref=Feed:MaplePrimes:Tagged With constants</link>
      <itunes:summary>&lt;p&gt;Hello!&lt;/p&gt;
&lt;p&gt;I'm trying to solve numerically an ODE system with piecewise. And this piecewise is very important for this task.&lt;/p&gt;
&lt;p&gt;This system describes behavior of a pulley with friction. There are some constants: m, c, g, mu and J. Values of this constants are not important.&lt;/p&gt;
&lt;p&gt;&amp;gt; sys := m*a(t) = piecewise(a(t) &amp;lt; a0, F0*time, a(t) &amp;gt;= a0, 0), v(t) = diff(x(t), t), a(t) = diff(v(t), t); &lt;br&gt; &amp;gt; m := 5; F0 := 10; a0 := 5;&lt;br&gt; &amp;gt; initialconditions := x(0) = 0, v(0) = 0;</itunes:summary>
      <description>&lt;p&gt;Hello!&lt;/p&gt;
&lt;p&gt;I'm trying to solve numerically an ODE system with piecewise. And this piecewise is very important for this task.&lt;/p&gt;
&lt;p&gt;This system describes behavior of a pulley with friction. There are some constants: m, c, g, mu and J. Values of this constants are not important.&lt;/p&gt;
&lt;p&gt;&amp;gt; sys := m*a(t) = piecewise(a(t) &amp;lt; a0, F0*time, a(t) &amp;gt;= a0, 0), v(t) = diff(x(t), t), a(t) = diff(v(t), t); &lt;br&gt; &amp;gt; m := 5; F0 := 10; a0 := 5;&lt;br&gt; &amp;gt; initialconditions := x(0) = 0, v(0) = 0;</description>
      <guid>103336</guid>
      <pubDate>Wed, 30 Mar 2011 08:58:53 Z</pubDate>
      <itunes:author>Macrohard</itunes:author>
      <author>Macrohard</author>
    </item>
    <item>
      <title>Extract the argument of a trigonometric function</title>
      <link>http://www.mapleprimes.com/questions/101690-Extract-The-Argument-Of-A-Trigonometric-Function?ref=Feed:MaplePrimes:Tagged With constants</link>
      <itunes:summary>&lt;p&gt;Regards,&lt;/p&gt;
&lt;p&gt;I have a very large equation which has an arctan(x,y). I need to be able to extract the arguments x,y and assign them in some variables.&lt;/p&gt;
&lt;p&gt;I have tried the solution given &lt;a href="http://www.mapleprimes.com/questions/40800-Extract-The-Argument-Of-A-Trig-Function%23comment75539"&gt;here&lt;/a&gt;.&lt;/p&gt;
&lt;p&gt;Unfortunately, that solution only works for constants, not equations.&lt;/p&gt;
&lt;p&gt;For example, if I use the proc given in there with arctan(10,11) it works. But if I use something like arctan...</itunes:summary>
      <description>&lt;p&gt;Regards,&lt;/p&gt;
&lt;p&gt;I have a very large equation which has an arctan(x,y). I need to be able to extract the arguments x,y and assign them in some variables.&lt;/p&gt;
&lt;p&gt;I have tried the solution given &lt;a href="http://www.mapleprimes.com/questions/40800-Extract-The-Argument-Of-A-Trig-Function%23comment75539"&gt;here&lt;/a&gt;.&lt;/p&gt;
&lt;p&gt;Unfortunately, that solution only works for constants, not equations.&lt;/p&gt;
&lt;p&gt;For example, if I use the proc given in there with arctan(10,11) it works. But if I use something like arctan...</description>
      <guid>101690</guid>
      <pubDate>Mon, 14 Feb 2011 20:56:21 Z</pubDate>
      <itunes:author>DarthVid</itunes:author>
      <author>DarthVid</author>
    </item>
  </channel>
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