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On the special values of Berndt's generalized -function
Yuan He
Source abstract
In this paper, we study the generalized -function considered by Berndt (1975). We introduce the generalized Apostol-Bernoulli polynomials and the generalized Apostol-Bernoulli functions, and establish some properties for them, including the Fourier series for these functions. We show that the values of Berndt's generalized -function at integers are explicitly evaluated in terms of the generalized Apostol-Bernoulli functions.
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