# Math Help - Integration to find the Fourier coefficients

1. ## 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.

2. 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