Some discrete Fourier transform pairs associated with the Lipschitz–Lerch Zeta function

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• 作者：Djurdje Cvijović ; H.M. Srivastava
• 关键词：Hurwitz&#x2013 ; Lerch Zeta function ; Lipschitz&#x2013 ; Lerch Zeta function ; Lerch Zeta function ; Hurwitz Zeta function ; Riemann Zeta function ; Legendre chi function ; Bernoulli polynomials ; Bernoulli numbers ; Discrete Fourier transform
• 刊名：Applied Mathematics Letters
• 出版年：2009
• 出版时间：July 2009
• 年：2009
• 卷：22
• 期：7
• 页码：1081-1084
• 全文大小：314 K

文摘

It is shown that there exists a companion formula to Srivastava’s formula for the Lipschitz–Lerch Zeta function [see H.M. Srivastava, Some formulas for the Bernoulli and Euler polynomials at rational arguments, Math. Proc. Cambridge Philos. Soc. 129 (2000) 77–84] and that together these two results form a discrete Fourier transform pair. This Fourier transform pair makes it possible for other (known or new) results involving the values of various Zeta functions at rational arguments to be easily recovered or deduced in a more general context and in a remarkably unified manner.