Mariusz Iwaniuk

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4 years, 64 days

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These are questions asked by Mariusz Iwaniuk

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))

Thanks.

fracdiff.mw

Hi all,

How to calculate this integral:

for k>0,m>0

Int(exp(-(1/2)*v/k)*v^3*exp((1/2)*v/m)*Ei(1, -(1000*I)*v+(1/2)*v/m), v = 0 .. infinity)

I'm  tried to take advantage of with(IntegrationTools) but I failed

and and I got a strange result ,like this:

Integral.mw

Hello.

I have a Pde solution in from of the sum.

pde := diff(u(x, t), t) = diff(u(x, t), x$2)

symbolic := pdsolve([pde, u(x, 0) = 1, u(0, t) = 0, u(1, t) = 0])

symbolic := u(x, t) = Sum(-(2*((-1)^_Z9-1))*sin(_Z9*Pi*x)*exp(-Pi^2*_Z9^2*t)/(Pi*_Z9), _Z9 = 1 .. infinity)

 

I tried a subs or eval command dosen't work.

 

Thanks.

pdex1.mw
 

restart

pde := diff(u(x, t), t) = diff(u(x, t), `$`(x, 2)):

ics := [u(x, 0) = 1, u(0, t) = 0, u(1, t) = 0]:

pds := pdsolve(pde, ics, numeric, time = t, range = 0 .. 1, spacestep = 1/4024, timestep = 1/4024):

symbolic := pdsolve([pde, u(x, 0) = 1, u(0, t) = 0, u(1, t) = 0])

u(x, t) = Sum(-2*((-1)^_Z9-1)*sin(_Z9*Pi*x)*exp(-Pi^2*_Z9^2*t)/(Pi*_Z9), _Z9 = 1 .. infinity)

(1)

eval(rhs(symbolic), `~`[_Z9] = n)

Sum(-2*((-1)^_Z9-1)*sin(_Z9*Pi*x)*exp(-Pi^2*_Z9^2*t)/(Pi*_Z9), _Z9 = 1 .. infinity)

(2)

subs(`~`[_Z9] = n, rhs(symbolic))

Sum(-2*((-1)^_Z9-1)*sin(_Z9*Pi*x)*exp(-Pi^2*_Z9^2*t)/(Pi*_Z9), _Z9 = 1 .. infinity)

(3)

subs[eval](`~`[_Z9] = n, rhs(symbolic))

Sum(-2*((-1)^_Z9-1)*sin(_Z9*Pi*x)*exp(-Pi^2*_Z9^2*t)/(Pi*_Z9), _Z9 = 1 .. infinity)

(4)

``


 

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