A note on Clebsch-Gordan integral, Fourier-Legendre expansions and closed form for hypergeometric series

Abstract

In this paper we show that a closed form formula for the generalized Clebsch-Gordan integral and the Fourier-Legendre expansion theory allow to evaluate hypergeometric series involving powers of the normalized central binomial coefficient $\frac{1}{4^n}\left(\genfrac{}{}{0ex}{}{2n}{n}\right)$.

Accepted in The Ramanujan Journal