Let
$$f(\alpha, \beta) = \int_0^{\infty} dx \: \frac{x^{\alpha}}{1+2 x \cos{(\pi \beta)} + x^2}$$
defined inside the unit square. Then we have $f(\alpha, \beta)=f(\beta, \alpha)$. But why?
Reference: https://math.stackexchange.com/questions/268789/symmetry-of-function-defined-by-integral
