Difficult integral...

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 Feynmann 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 wich is not much better.