You could investigate the behavior of the integrand as xi approached negative infinity thanks to the function limit(). For instance,

limit(exp(-xi^2*(3*n+xi)/(6*n^2+6*xi*n+xi^2)), xi = -infinity)

Regards, -- Jean-Marc

You could investigate the behavior of the integrand as xi approached negative infinity thanks to the function limit(). For instance,

limit(exp(-xi^2*(3*n+xi)/(6*n^2+6*xi*n+xi^2)), xi = -infinity)

Regards, -- Jean-Marc

What version of Maple are you using? Have you tried with a fresh kernel (new session or restart)? Acer's code works as expected on my Maple 12.02 system.

restart;
T := module() option package;
export sin, cos, arcsin, arccos;
  sin := proc(x) :-sin(x*Pi/180); end proc:
  cos := proc(x) :-cos(x*Pi/180); end proc:
  arcsin := proc(x) 180/Pi * :-arcsin(x); end proc:
  arccos := proc(x) 180/Pi * :-arccos(x); end proc:
end module:
with(T);
                         [arccos, arcsin, cos, sin]

map(sin, [0, 30, 45, 90]);
map(arcsin, %);

                             [   1  1  (1/2)   ]
                             [0, -, - 2     , 1]
                             [   2  2          ]
                               [0, 30, 45, 90]

map(:-sin, [0, Pi/6, Pi/4, Pi/2]);
map(:-arcsin, %);

                             [   1  1  (1/2)   ]
                             [0, -, - 2     , 1]
                             [   2  2          ]
                            [   1     1     1   ]
                            [0, - Pi, - Pi, - Pi]
                            [   6     4     2   ]

map(cos, [0, 30, 45, 90]);
map(arccos, %);

                         [   1  (1/2)  1  (1/2)   ]
                         [1, - 3     , - 2     , 0]
                         [   2         2          ]
                               [0, 30, 45, 90]

map(:-cos, [0, Pi/6, Pi/4, Pi/2]);
map(:-arccos, %);

                         [   1  (1/2)  1  (1/2)   ]
                         [1, - 3     , - 2     , 0]
                         [   2         2          ]
                            [   1     1     1   ]
                            [0, - Pi, - Pi, - Pi]
                            [   6     4     2   ]

kernelopts(version);

        Maple 12.02, APPLE UNIVERSAL OSX, Dec 10 2008 Build ID 377066

Regards, -- Jean-Marc

What version of Maple are you using? Have you tried with a fresh kernel (new session or restart)? Acer's code works as expected on my Maple 12.02 system.

restart;
T := module() option package;
export sin, cos, arcsin, arccos;
  sin := proc(x) :-sin(x*Pi/180); end proc:
  cos := proc(x) :-cos(x*Pi/180); end proc:
  arcsin := proc(x) 180/Pi * :-arcsin(x); end proc:
  arccos := proc(x) 180/Pi * :-arccos(x); end proc:
end module:
with(T);
                         [arccos, arcsin, cos, sin]

map(sin, [0, 30, 45, 90]);
map(arcsin, %);

                             [   1  1  (1/2)   ]
                             [0, -, - 2     , 1]
                             [   2  2          ]
                               [0, 30, 45, 90]

map(:-sin, [0, Pi/6, Pi/4, Pi/2]);
map(:-arcsin, %);

                             [   1  1  (1/2)   ]
                             [0, -, - 2     , 1]
                             [   2  2          ]
                            [   1     1     1   ]
                            [0, - Pi, - Pi, - Pi]
                            [   6     4     2   ]

map(cos, [0, 30, 45, 90]);
map(arccos, %);

                         [   1  (1/2)  1  (1/2)   ]
                         [1, - 3     , - 2     , 0]
                         [   2         2          ]
                               [0, 30, 45, 90]

map(:-cos, [0, Pi/6, Pi/4, Pi/2]);
map(:-arccos, %);

                         [   1  (1/2)  1  (1/2)   ]
                         [1, - 3     , - 2     , 0]
                         [   2         2          ]
                            [   1     1     1   ]
                            [0, - Pi, - Pi, - Pi]
                            [   6     4     2   ]

kernelopts(version);

        Maple 12.02, APPLE UNIVERSAL OSX, Dec 10 2008 Build ID 377066

Regards, -- Jean-Marc

What version of Maple are you using? The example I posted works fine on Maple 12.02.

> kernelopts(version);

        Maple 12.02, APPLE UNIVERSAL OSX, Dec 10 2008 Build ID 377066

> interface(version);

Standard Worksheet Interface, Maple 12.02, Mac OS X, 
December 10 2008 Build ID 377066

Regards, -- Jean-Marc

What version of Maple are you using? The example I posted works fine on Maple 12.02.

> kernelopts(version);

        Maple 12.02, APPLE UNIVERSAL OSX, Dec 10 2008 Build ID 377066

> interface(version);

Standard Worksheet Interface, Maple 12.02, Mac OS X, 
December 10 2008 Build ID 377066

Regards, -- Jean-Marc

The solution depends on the value of the coefficient a. If a is positive then the integral evaluates to 4*Pi*sinh(a)/a. For your second question, you could try the free web service Wolfram Mathemartica Online Integrator. Also, The Wolfram Functions Site might be useful. Regards, -- Jean-Marc

The solution depends on the value of the coefficient a. If a is positive then the integral evaluates to 4*Pi*sinh(a)/a. For your second question, you could try the free web service Wolfram Mathemartica Online Integrator. Also, The Wolfram Functions Site might be useful. Regards, -- Jean-Marc

You post some acutal code and the output that results from evaluating it. For instance, one can see that the following works like a charm:

> restart;
> with(Statistics):
> X:=Sample(Normal(0,1),10):
> h_X:=FrequencyTable(X);
> h_X[1..,2];

        [ -1.656577251 .. -1.238700840   1.  10.00000000  1.   10.00000000]
        [                                                                 ]
        [-1.238700840 .. -0.8208244286   2.  20.00000000  3.   30.00000000]
        [                                                                 ]
        [-0.8208244286 .. -0.4029480176  1.  10.00000000  4.   40.00000000]
        [                                                                 ]
        [-0.4029480176 .. 0.01492839343  0.      0.       4.   40.00000000]
        [                                                                 ]
        [0.01492839343 .. 0.4328048045   1.  10.00000000  5.   50.00000000]
 h_X := [                                                                 ]
        [ 0.4328048045 .. 0.8506812155   2.  20.00000000  7.   70.00000000]
        [                                                                 ]
        [ 0.8506812155 .. 1.268557627    2.  20.00000000  9.   90.00000000]
        [                                                                 ]
        [  1.268557627 .. 1.686434038    0.      0.       9.   90.00000000]
        [                                                                 ]
        [  1.686434038 .. 2.104310449    0.      0.       9.   90.00000000]
        [                                                                 ]
        [  2.104310449 .. 2.522186860    1.  10.00000000  10.  100.0000000]

                  [1., 2., 1., 0., 1., 2., 2., 0., 0., 1.]

Regards, -- Jean-Marc

You post some acutal code and the output that results from evaluating it. For instance, one can see that the following works like a charm:

> restart;
> with(Statistics):
> X:=Sample(Normal(0,1),10):
> h_X:=FrequencyTable(X);
> h_X[1..,2];

        [ -1.656577251 .. -1.238700840   1.  10.00000000  1.   10.00000000]
        [                                                                 ]
        [-1.238700840 .. -0.8208244286   2.  20.00000000  3.   30.00000000]
        [                                                                 ]
        [-0.8208244286 .. -0.4029480176  1.  10.00000000  4.   40.00000000]
        [                                                                 ]
        [-0.4029480176 .. 0.01492839343  0.      0.       4.   40.00000000]
        [                                                                 ]
        [0.01492839343 .. 0.4328048045   1.  10.00000000  5.   50.00000000]
 h_X := [                                                                 ]
        [ 0.4328048045 .. 0.8506812155   2.  20.00000000  7.   70.00000000]
        [                                                                 ]
        [ 0.8506812155 .. 1.268557627    2.  20.00000000  9.   90.00000000]
        [                                                                 ]
        [  1.268557627 .. 1.686434038    0.      0.       9.   90.00000000]
        [                                                                 ]
        [  1.686434038 .. 2.104310449    0.      0.       9.   90.00000000]
        [                                                                 ]
        [  2.104310449 .. 2.522186860    1.  10.00000000  10.  100.0000000]

                  [1., 2., 1., 0., 1., 2., 2., 0., 0., 1.]

Regards, -- Jean-Marc

An afterthought, but reading more carefully your code, I have realized that my previous post might not be the solution to your actual problem: you are using D as a parameter (in this case the * is OK); however this is a very poor choice for a variable name since it is already defined as the differential operator (which brought my initial remark about the syntax and missing parenthesis). See help("D") for more info. Therefore, you might want to change this parameter name into something else that is not already defined as a builtin operator of function. Regards, -- Jean-Marc

An afterthought, but reading more carefully your code, I have realized that my previous post might not be the solution to your actual problem: you are using D as a parameter (in this case the * is OK); however this is a very poor choice for a variable name since it is already defined as the differential operator (which brought my initial remark about the syntax and missing parenthesis). See help("D") for more info. Therefore, you might want to change this parameter name into something else that is not already defined as a builtin operator of function. Regards, -- Jean-Marc

Pay close attention to the syntax and do not hesitate to consult the online help pages and browse the examples for the Maple commands. View 97_combiningmultigraph.mw on MapleNet or Download 97_combiningmultigraph.mw
View file details

> restart;

> with(plots):

> points1 := [[0, 3.9], [10, 5.3], [20, 7.2], [30, 9.6], [40, 12.9], [50, 17.1], [60, 23.1], [70, 31.4], [80, 38.6], [90, 50.2], [100, 62.9]]:

> p1 := pointplot(points1);

> p1;

> points2 := [[110, 76.0], [120, 92.0], [130, 105.7], [140, 122.8], [150, 131.7], [160, 150.7], [170, 179.0], [180, 205.0], [190, 226.5], [200, 248.7]]:

> p2 := pointplot(points2);

> p2;

> p3 := plot((901.1/(3.9+227.1*exp(-0.30e-1*(x+10)))-901.1/(3.9+227.1*exp(-0.30e-1*x)))*(1/10), color = blue);

> p3;

> p4 := plot((60447.9/(131.7+327.3*exp(-0.225e-1*(x+10)+3.3750))-60447.9/(131.7+327.3*exp(-0.225e-1*x+3.3750)))*(1/10), color = red);

> p4;

> display(p1,p2,p3,p4);

>

This post was generated using the MaplePrimes File Manager

View 97_combiningmultigraph.mw on MapleNet or Download 97_combiningmultigraph.mw
View file details

Regards, -- Jean-Marc

Pay close attention to the syntax and do not hesitate to consult the online help pages and browse the examples for the Maple commands. View 97_combiningmultigraph.mw on MapleNet or Download 97_combiningmultigraph.mw
View file details

> restart;

> with(plots):

> points1 := [[0, 3.9], [10, 5.3], [20, 7.2], [30, 9.6], [40, 12.9], [50, 17.1], [60, 23.1], [70, 31.4], [80, 38.6], [90, 50.2], [100, 62.9]]:

> p1 := pointplot(points1);

> p1;

> points2 := [[110, 76.0], [120, 92.0], [130, 105.7], [140, 122.8], [150, 131.7], [160, 150.7], [170, 179.0], [180, 205.0], [190, 226.5], [200, 248.7]]:

> p2 := pointplot(points2);

> p2;

> p3 := plot((901.1/(3.9+227.1*exp(-0.30e-1*(x+10)))-901.1/(3.9+227.1*exp(-0.30e-1*x)))*(1/10), color = blue);

> p3;

> p4 := plot((60447.9/(131.7+327.3*exp(-0.225e-1*(x+10)+3.3750))-60447.9/(131.7+327.3*exp(-0.225e-1*x+3.3750)))*(1/10), color = red);

> p4;

> display(p1,p2,p3,p4);

>

This post was generated using the MaplePrimes File Manager

View 97_combiningmultigraph.mw on MapleNet or Download 97_combiningmultigraph.mw
View file details

Regards, -- Jean-Marc

See ?selection on the online help for more info.

> lst:=[seq([seq(i+10*j,i=1..5)],j=1..4)];

 lst := [[11, 12, 13, 14, 15], [21, 22, 23, 24, 25], [31, 32, 33, 34, 35], 

   [41, 42, 43, 44, 45]]

> lst[1..,2]; # Take the second column of each row

                              [12, 22, 32, 42]

Regards, -- Jean-Marc