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Two-dimensional series evaluations via the elliptic functions of Ramanujan and Jacobi

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Abstract

We evaluate in closed form, for the first time, certain classes of double series, which are remindful of lattice sums. Elliptic functions, singular moduli, class invariants, and the Rogers–Ramanujan continued fraction play central roles in our evaluations.

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Authors and Affiliations

  1. Department of Mathematics, University of Illinois, 1409 West Green St., Urbana, IL, 61801, USA

    Bruce C. Berndt

  2. 2942 Ave. del Conquistador, Tucson, AZ, 85749-9304, USA

    George Lamb

  3. Département de Mathématiques et Statistique, Université de Montréal, CP6128, Succ. Cenrte-Ville, Montréal, QC, H3T 1J4, Canada

    Mathew Rogers

Authors
  1. Bruce C. Berndt
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  2. George Lamb
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  3. Mathew Rogers
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Corresponding author

Correspondence to Bruce C. Berndt.

Additional information

The research of Bruce C. Berndt was supported by National Security Agency grant H98230-11-1-0200.

The research of Mathew Rogers was supported by National Science Foundation grant DMS-0803107.

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Berndt, B.C., Lamb, G. & Rogers, M. Two-dimensional series evaluations via the elliptic functions of Ramanujan and Jacobi. Ramanujan J 29, 185–198 (2012). https://doi.org/10.1007/s11139-011-9351-9

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  • DOI: https://doi.org/10.1007/s11139-011-9351-9

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