Jackson's integral of multiple Hurwitz-Lerch zeta functions and multiple gamma functions

2014/08/14 by Su Hu, Daeyeoul Kim, Hu, Su +3
Mathematics · #11M35 #35B15 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1408.3243

openalex publication_date 2014/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using the Jackson integral, we obtain the q-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 q-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.

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