A generating function of the squares of Legendre polynomials

Abstract: We relate a one-parametric generating function for the squares of Legendre polynomials to an arithmetic hypergeometric series whose parametrisation by a level 7 modular function was recently given by Shaun Cooper. By using this modular parametrisation we resolve a subfamily of identities involving $1/\pi$ which was experimentally observed by Zhi-Wei Sun.