The Lerch zeta function as a fractional derivative
Volume 118 / 2019
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.
