Jackson's integral of multiple Hurwitz-Lerch zeta functions and multiple gamma functions
Number Theory
2018-08-10 v3
Abstract
Using the Jackson integral, we obtain the -integral analogue of the Raabe type formulas for Barnes multiple Hurwitz-Lerch zeta functions and Barnes and Vardi's multiple gamma functions. Our results generalize -integral analogue of the Raabe type formulas for the Hurwitz zeta functions and log gamma functions in [N. Kurokawa, K. Mimachi, and M. Wakayama, Jackson's integral of the Hurwitz zeta function, Rend. Circ. Mat. Palermo (2) 56 (2007), no. 1, 43--56]. During the proof we also obtain a new formula on the relationship between the higher and lower orders Hurwitz zeta functions.
Keywords
Cite
@article{arxiv.1408.3243,
title = {Jackson's integral of multiple Hurwitz-Lerch zeta functions and multiple gamma functions},
author = {Su Hu and Daeyeoul Kim and Min-Soo Kim},
journal= {arXiv preprint arXiv:1408.3243},
year = {2018}
}
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14 pages