Analytic continuation of the series
Abstract: The series ranging over all integers except both zero, for an integer greater than two is well known from the theory of elliptic functions and modular forms. In this paper, we show that this series defines an analytic function for and which has an analytic continuation to all values of . It is then shown that satisfies a functional equation under the transformation , and finally as an application some numerical results are obtained.
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Keywords: Analytic continuation, modular form, functional equation
Article copyright: © Copyright 1971 American Mathematical Society