# Integration to find the Fourier coefficients

• March 4th 2010, 01:43 AM
Gaudium
Integration to find the Fourier coefficients
Hi, I want to calculate the Fourier series expansion of

f(x)= a sin(x) / (1-2 a cos(x) + a^2), where |a|<1 and -pi < x <pi,

but I cannot integrate the function "cos(nx) f(x)". Is there a trick for this integration. Thanks.
• March 4th 2010, 09:22 PM
CaptainBlack
Quote:

Originally Posted by Gaudium
Hi, I want to calculate the Fourier series expansion of

f(x)= a sin(x) / (1-2 a cos(x) + a^2), where |a|<1 and -pi < x <pi,

but I cannot integrate the function "cos(nx) f(x)". Is there a trick for this integration. Thanks.

Observe that:

$f(x)=\frac{d}{dx} \left[ \frac{1}{2}\ln(1-2a \cos(x)+a^2)\right]$

then integration by parts will help

CB