Mariusz Iwaniuk

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These are questions asked by Mariusz Iwaniuk

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 ?


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.

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?

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?


Thank you in advance.

I am looking forward to hearing from you.

I have recently been working on a problem using fractional calculus and have come across something in Maple's fracdiff  command that makes no sense to me.

fracdiff(1, x, 1/2) = 0

It should be:     1/(sqrt(x)*sqrt(Pi))


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