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An elementary proof of Ramanujan’s circular summation formula and its generalizations

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Abstract

In this paper, we give a completely elementary proof of Ramanujan’s circular summation formula of theta functions and its generalizations given by S.H. Chan and Z.-G. Liu, who used the theory of elliptic functions. In contrast to all other proofs, our proofs are elementary. An application of this summation formula is given.

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  1. University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA

    Ping Xu

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  1. Ping Xu
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Correspondence to Ping Xu.

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Xu, P. An elementary proof of Ramanujan’s circular summation formula and its generalizations. Ramanujan J 27, 409–417 (2012). https://doi.org/10.1007/s11139-011-9364-4

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  • DOI: https://doi.org/10.1007/s11139-011-9364-4

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