The Lerch zeta function as a fractional derivative
arXiv:1804.07936 · 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.
10 pages; peer-reviewed and accepted in Banach Center Publications as part of proceedings of Number Theory Week 2017