Fractional differential relations for the Lerch zeta function
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- May 2020
- DOI:
- 10.48550/arXiv.2006.01046
- arXiv:
- arXiv:2006.01046
- Bibcode:
- 2020arXiv200601046F
- Keywords:
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- Mathematics - Number Theory;
- Mathematics - Complex Variables