A GENERATING FUNCTION OF THE SQUARES OF LEGENDRE POLYNOMIALS

Author:

ZUDILIN WADIM

Abstract

AbstractWe 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 Cooper. By using this modular parametrisation we resolve a subfamily of identities involving$1/ \pi $which was experimentally observed by Sun.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Cited by 12 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. On the Persson-Strang’s Identity for the Legendre Polynomials;European Journal of Theoretical and Applied Sciences;2023-11-01

2. Ramanujan-type $$1/\pi $$-series from bimodular forms;The Ramanujan Journal;2022-01-07

3. New series for powers of \begin{document}$ \pi $\end{document} and related congruences;Electronic Research Archive;2020

4. Short Walk Adventures;Springer Proceedings in Mathematics & Statistics;2020

5. An Analytic Method for Computing the Infinite Sums Occurring in the Geoelastic Disk Load Problem;Journal of Geophysical Research: Solid Earth;2019-02

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