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/π which was experimentally observed by Zhi-Wei Sun.
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