# Fourier coefficients in string theory

1. Jan 30, 2015

### moriheru

If a function f'(u) has fourier coefficients anμ and bnμ, by integration one can make new coefficients Anμ ,Bnμ which include constants of integration.
My question how can I verify that :

Anμcos nτ + Bnμ sin nτ= -i/2 ((Bnμ) -Anμi) einτ- (Bnμ-iAnμ) e-inτ

I assume this is the complex form of fourier series, but anyway

thanks for any clarifications.

2. Jan 30, 2015

### mathman

The relationship is purely mathematical.
$e^{ix}=cos(x)+isin(x)$. Substitute in the right side and you get the left side.

3. Jan 31, 2015

### moriheru

Thanks mathman.