Fourier series expansion $\sin^{2m-1} (x)$

107 Views Asked by At

I can't calculate the coefficients of the Fourier. Integral turns out to be very difficult. Are there any tips on how to calculate them more easily? $\sin^{2m-1} (x), m \in \mathbb{N}$

Also I need to find the sum of the row $$\sum \limits_{n=1}^{\infty} (C^{m-n}_{2m-1})^2 $$

m here is the same as for sin.