The Lerch zeta function as a fractional derivative

Volume 118 / 2019

Arran Fernandez Banach Center Publications 118 (2019), 113-124 MSC: 11M35; 26A33. DOI: 10.4064/bc118-7

Abstract

We derive and prove a new formulation of the Lerch zeta function as a fractional derivative of an elementary function. We demonstrate how this formulation interacts very naturally with basic known properties of Lerch zeta, and use the functional equation to obtain a second formulation in terms of fractional derivatives.

Authors

  • Arran FernandezDepartment of Applied Mathematics and Theoretical Physics
    University of Cambridge
    Wilberforce Road
    CB3 0WA, United Kingdom
    and
    Department of Mathematics
    Eastern Mediterranean University
    Famagusta, North Cyprus
    via Mersin 10
    Turkey
    e-mail

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