## 1506 Reputation

8 years, 304 days

## Differentiation and Integration with Int...

Maple 2018

In Maple 2018 help written:

The interpolation methods available in the Interpolation package all work as follows. First, the user calls one of the commands in the package, submitting the input points and the values at these points. This returns an object encapsulating all the data and options submitted. This object can then be used like a normal mathematical function, e.g. for plotting, integration, or just to evaluate at a given point.

The Interpolation[Interpolate] command was introduced in Maple 2018

My test example:

with(Interpolation):

points := [seq(x, x = 0 .. 10, 1)]; data := [seq(sqrt(1.+x^2), x = 0 .. 10, 1)];

f := Interpolate(points, data);

f(1); # OK works :).

int(f(x), x = 0 .. 1); # Not working ?

int(f(x), x = 0 .. 1,numeric); # Not working ?

eval(diff(f(x), x), x = 2);# Not working ?

plot(f(x), x = 0 .. 10);#  OK works :)

plot([f(x), diff(f(x), x)], x = 0 .. 10);# Not working ?

plot([f, diff(f, x)], 0 .. 10);# Only a half  working ?

Thanks.

## pdsolve: PDE by series?...

Maple 2018

I have PDE i trying to solve the equation using series.

pdsolve(diff(u(x, y), x, x)+diff(u(x, y), y, y) = Pi, series, order = 2);

Give me: "Error, (in DifferentialAlgebra:-RosenfeldGroebner) unexpected occurrence of the non-rational constants {Pi} in the given input" ?

pdsolve(diff(u(x, y), x, x)+diff(u(x, y), y, y) =gamma, series, order = 2);#gamma = 0.5772156649,Gives ERROR ?

If I  change instead of Pi is e or exp(1) works fine.

pdsolve(diff(u(x, y), x, x)+diff(u(x, y), y, y) = exp(1), series, order = 2);#OK.

It's a bug, design or  something else ?

## Calculate integral?...

Maple 2018

int(exp(-sec(t))*cos(t)/(-1/4+sin(t)^2), t = 0 .. (1/2)*Pi, CauchyPrincipalValue = true, numeric = true);

Returns unevaluated for me.

```I tried all the methods in HELP documentation and I failed.
Integral is singular at point 1/4.

```

Thank you.

## Simplifying the polylogs....

Maple 2017

I have a expression with polylog functions.I want to simplifying to Pi's constans.I tired with:

```1. simplify
2. convert```

but seems dosen't work:

```simplify(sum((sin(k)/k)^7, k = 0 .. infinity))

#1+(1/128*I)*polylog(7, exp(7*I))-(7/128*I)*polylog(7, exp(5*I))+(21/128*I)*polylog(7, exp(3*I))-
(35/128*I)*polylog(7, exp(I))+(35/128*I)*polylog(7, exp(-I))-(21/128*I)*polylog(7, exp(-3*I))+
(7/128*I)*polylog(7, exp(-5*I))-(1/128*I)*polylog(7, exp(-7*I))```

Mathematica give me:

How to do it in Maple?

## Problem with finite sum. Negative upper ...

Maple 2016

Hi Dears,

I'm have a code like this:

sum(-GAMMA(k+1, x), k = 0 .. -2) and Maple give me : Ei(1, x).

How to check that answer is correct?