Fourier Series based on 2 limits for x

  • Thread starter mullzer
  • Start date
  • #1
11
0
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.
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
25,836
251
welcome to pf!

hi mullzer! welcome to pf! :smile:

(have a pi: π and an infinity: ∞ and try using the X2 and X2 icons just above the Reply box :wink:)
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 :smile:
 
  • #3
11
0
Thanks very much for the help. The substitution of the integral worked.. and my the test went well in the end!
 

Related Threads on Fourier Series based on 2 limits for x

  • Last Post
Replies
4
Views
7K
  • Last Post
Replies
8
Views
70K
  • Last Post
Replies
2
Views
6K
  • Last Post
Replies
6
Views
1K
  • Last Post
Replies
14
Views
17K
Replies
8
Views
5K
Replies
2
Views
310
Replies
2
Views
12K
Replies
1
Views
1K
  • Last Post
Replies
1
Views
2K
Top