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A GENERATING FUNCTION OF THE SQUARES OF LEGENDRE POLYNOMIALS

Published online by Cambridge University Press:  22 March 2013

WADIM ZUDILIN*
Affiliation:
School of Mathematical and Physical Sciences, The University of Newcastle, Callaghan, NSW 2308, Australia
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Abstract

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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 involving $1/ \pi $ which was experimentally observed by Sun.

Type
Research Article
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

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