A GENERATING FUNCTION OF THE SQUARES OF LEGENDRE POLYNOMIALS

@article{Zudilin2014AGF,
  title={A GENERATING FUNCTION OF THE SQUARES OF LEGENDRE POLYNOMIALS},
  author={Wadim Zudilin},
  journal={Bulletin of The Australian Mathematical Society},
  year={2014},
  volume={89},
  pages={125-131}
}
  • Wadim Zudilin
  • Published 2014
  • Mathematics, Physics
  • Bulletin of The Australian Mathematical Society
  • 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 S. Cooper. By using this modular parametrisation we resolve a subfamily of identities involving \(1/\pi\) which was experimentally observed by Z.-W. Sun. 10.1017/S0004972713000233 

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