Fractional differential relations for the Lerch zeta function
Number Theory
2020-06-02 v1 Complex Variables
Abstract
Starting from a recent result expressing the Lerch zeta function as a fractional derivative, we consider further fractional derivatives of the Lerch zeta function with respect to different variables. We establish a partial differential equation, involving an infinite series of fractional derivatives, which is satisfied by the Lerch zeta function.
Cite
@article{arxiv.2006.01046,
title = {Fractional differential relations for the Lerch zeta function},
author = {Arran Fernandez and Jean-Daniel Djida},
journal= {arXiv preprint arXiv:2006.01046},
year = {2020}
}