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 ${\displaystyle \frac{1}{4^{n}}\dbinom{2n}{n}}$.