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Legendre polynomials and Ramanujan-type series for 1/π

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Abstract

We resolve a family of recently observed identities involving 1/π using the theory of modular forms and hypergeometric series. In particular, we resort to a formula of Brafman which relates a generating function of the Legendre polynomials to a product of two Gaussian hypergeometric functions. Using our methods, we also derive some new Ramanujan-type series.

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Authors and Affiliations

  1. Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore, 117543, Singapore

    Heng Huat Chan

  2. School of Mathematical and Physical Sciences, The University of Newcastle, Callaghan, NSW, 2308, Australia

    James Wan & Wadim Zudilin

Authors
  1. Heng Huat Chan
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  2. James Wan
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  3. Wadim Zudilin
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Corresponding author

Correspondence to Heng Huat Chan.

Additional information

On Jon Borwein’s 60th birthday

The third author is supported by Australian Research Council grant DP110104419.

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Chan, H.H., Wan, J. & Zudilin, W. Legendre polynomials and Ramanujan-type series for 1/π . Isr. J. Math. 194, 183–207 (2013). https://doi.org/10.1007/s11856-012-0081-5

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  • DOI: https://doi.org/10.1007/s11856-012-0081-5

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