School of Mathematical and Physical Sciences, The University of Newcastle, Callaghan, NSW 2308, Australia
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 Cooper. By using this modular parametrisation we resolve a subfamily of identities involvingwhich was experimentally observed by Sun.
(Received November 28 2012)
(Accepted February 06 2013)
(Online publication March 22 2013)
2010 Mathematics subject classification
Keywords and phrases
The author was supported by the Australian Research Council.