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


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.


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

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