Fourier coefficients in string theory

[moriheru]

If a function f'(u) has Fourier coefficients a_n^μ and b_n^μ, by integration one can make new coefficients A_n^μ ,B_n^μ which include constants of integration.
My question how can I verify that :

A_n^μcos nτ + B_n^μ sin nτ= -i/2 ((B_n^μ) -A_n^μi) e^inτ- (B_n^μ-iA_n^μ) e^-inτ

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

thanks for any clarifications.

 

[mathman]

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

 

[moriheru]

Thanks mathman.