Analytic continuation of the doubly-periodic Barnes zeta function
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摘要
The aim of this work is to study the analytic continuation of the doubly-periodic Barnes zeta function. By using a suitable complex integral representation as a starting point we find the meromorphic extension of the doubly periodic Barnes zeta function to the entire complex plane in terms of a real integral containing the Hurwitz zeta function and the first Jacobi theta function. These allow us to explicitly give expressions for the derivative at all non-positive integer points.
论文关键词:Analytic continuation,Barnes zeta function,Special functions
论文评审过程:Available online 30 July 2013.
论文官网地址:https://doi.org/10.1016/j.amc.2013.06.092