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Difficult integral... 
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#1
Aug404, 10:03 AM

P: 215

I have problems calculating the integral (here 8 means infinite)
Int(ci8,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. 


#2
Aug404, 10:14 AM

P: 160

what is the analitic expression of R?



#3
Aug504, 04:59 AM

P: 215

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. 


#4
Aug504, 05:29 AM

Sci Advisor
HW Helper
P: 9,396

Difficult integral...
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



#5
Aug604, 04:33 AM

P: 215

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. 


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