Integration of monomials over the unit spere and unit ball in $R^n$

Calixto P. Calderon, Alberto Torchinsky

We compute the integral of monomials of the form $x^{2\beta }$ over the unit sphere and the unit ball in $R^n$ where $\beta =({\beta }_1,...,{\beta }_n)$ is a multi-index with real components $β_k > -1/2…