Calculating Difficult Integral: Int(-8,8)iduexp(cx)exp(iu)/(c+iu)R(c+iu)

[eljose79]

I have problems calculating the integral (here 8 means infinite)

Int(c-i8,c+i8)dsexp(sx)/sR(s) where R(sd) is Riemann,s function i make the change of variable s=c+iu so the new limits are

Int(-8,8)iduexp(cx)exp(iu)/(c+iu)R(c+iu) now what numerical method could i use to calculate it?..thanks.

 

[Feynman]

what is the analitic expression of R?

 

[eljose79]

R(s) is Riemann,s zeta function R(s)=1+2^s+3^s+4^s+....

hope no Feynman you could give me a hand.

 

[matt grime]

if only you knew where all the poles were. and if you took a couple of minutes to learn some basic latex your posts would be easier to read. try the thread in general physics

 

[eljose79]

Latex is hard for me to understand,there are lots opf instruction in fact in the integral...we could do..

Int(-8,8)duexp(iux)/R(c+iu) instead of putting 8 (8=infinite) put N with N big (for example N=10^200000000000) make the change of variable u=Nt then the integral becomes:

Int(-1,1)Ndtexp(iNtx)/R(c+iNt) now the integral (-1,1) can be computed approximately using Gaussian integration.

Yes you could solve it knowing where the poles are but for the function 1/R(s) there are infinite poles so we substitute the problme of calculating an integral to the problem of calculating an infinite series which is not much better.