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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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