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arXiv · 1210.2493

A generating function of the squares of Legendre polynomials

Wadim Zudilin
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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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Wadim Zudilin. 2012-12-04. A generating function of the squares of Legendre polynomials. https://doi.org/10.1017/s0004972713000233

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