Wadim Zudilin
Published 2012-10-09, updated 2012-12-04Version 2
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.
Comments: 7 pages
Journal: Bull. Austral. Math. Soc. 89:1 (2014) 125--131
Coupling of the Legendre polynomials with kernels $|x-y|^α$ and $\ln|x-y|$
On a pointwise inequality for even Legendre polynomials in high dimensional spheres
Derivatives with respect to the order of the Legendre Polynomials
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