A generating function of the squares of Legendre polynomials

W. Zudilin


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 S. Cooper. By using this modular parametrisation we resolve a subfamily of identities involving \(1/\pi\) which was experimentally observed by Z.-W. Sun.



\(\pi\), Legendre polynomial, generating series, binomial sum, modular function

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Bulletin of the Aust. Math. Soc., copyright Australian Mathematical Publishing Association Inc.