Another discrete Fourier transform pairs associated with the Lipschitz-Lerch zeta function

Abstract

It is demonstrated that the alternating Lipschitz-Lerch zeta function and the alternating Hurwitz zeta function constitute a discrete Fourier transform pair. This discrete transform pair makes it possible to deduce, as special cases and consequences, many ( mainly new) transformation relations involving the values at rational arguments of alternating variants of various zeta functions, such as the Lerch and Hurwitz zeta functions and Legendre chi function. (C) 2011 Elsevier Inc. All rights reserved.