# Fourier Series based on 2 limits for x

i have an exam in these kind of questions in a few days so i was pracitsing a a few problems but I can't do them!
Any help would be appreciated.

Calculate the fourier series for f(x) when f(x) = 0, on -pi <= x <= 0, and f(x) = coshx, on 0 <= x <= pi.
and show that SUM (from n=1 to infinity) 1/(1+n^2)= (1/2)((pi/tanhx) - 1)

So far i have that A0 = sinhx. When i try to integrate An, i get stuck at the integral of coshx cosx dx. i tried changing coshx into exponential form but i still end up in an endless circle of integration by parts.

tiny-tim
Homework Helper
welcome to pf!

hi mullzer! welcome to pf!

(have a pi: π and an infinity: ∞ and try using the X2 and X2 icons just above the Reply box )
When i try to integrate An, i get stuck at the integral of coshx cosx dx. i tried changing coshx into exponential form but i still end up in an endless circle of integration by parts.

you should get something like ∫ excosx dx = something - ∫ excosx dx …

now just put the second integral over on the LHS

Thanks very much for the help. The substitution of the integral worked.. and my the test went well in the end!