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

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

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Article ID: iaor20121883
Volume: 218
Issue: 12
Start Page Number: 6744
End Page Number: 6747
Publication Date: Feb 2012
Journal: Applied Mathematics and Computation
Authors:
Keywords: Lipschitz functions, Fourier transform
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.

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