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.

7 pages

References in corpus (2)

• A solution of Sun's $520 challenge concerning 520/pi
• Lost in translation

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• Crouching AGM, Hidden Modularity
• Equilibration properties of small quantum systems: further examples
• Ramanujan-type $1/\pi$-series from bimodular forms