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A simple proof of Ramanujan’s summation of the1ψ1

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Abstract

A simple proof by functional equations is given for Ramanujan’s1 ψ 1 sum. Ramanujan’s sum is a useful extension of Jacobi's triple product formula, and has recently become important in the treatment of certain orthogonal polynomials defined by basic hypergeometric series.

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Authors and Affiliations

  1. Pennsylvania State University, 16802, University Park, Pennsylvania, USA

    George E. Andrews & Richard Askey

  2. University of Wisconsin, 53706, Madison, Wisconsin, USA

    George E. Andrews & Richard Askey

Authors
  1. George E. Andrews
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  2. Richard Askey
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Additional information

The work of the first author was partially sponsored by the United States Army under Contract No. DAAG29-75-C-0024 and NSF Grant 74-07282 and that of the second author was partially supported by NSF Grant MPS 75-06687 AO2.

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Andrews, G.E., Askey, R. A simple proof of Ramanujan’s summation of the1ψ1 . Aeq. Math. 18, 333–337 (1978). https://doi.org/10.1007/BF03031684

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  • DOI: https://doi.org/10.1007/BF03031684

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