The title says everything. I'm studying fourier series and I've stumbled upon this question:
find the fourier series of $f(x) = e^{r\cos x} \cos(r\sin x)$.
So that i need to integrate this function from $-\pi$ to $\pi$
I've tried integration by parts and a few u substitutions and got nowhere.
Best Answer
Hint: first note that $f(x)$ is the real part of $e^{r \cos x} e^{i r \sin x} = e^{r e^{ix}}$. Expand the "outer" exponential in a series...