Jackson's integral of multiple Hurwitz–Lerch zeta functions and multiple gamma functions
Copyright policy )Jackson's integral of multiple Hurwitz–Lerch zeta functions and multiple gamma functions
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.
14 pages
- Jeonbuk National University Korea (Republic of)
- Kyungnam University Korea (Republic of)
- South China University of Technology China (People's Republic of)
multiple Hurwitz-Lerch zeta function, Raabe type formula, Mathematics - Number Theory, FOS: Mathematics, Jackson integral, Hurwitz and Lerch zeta functions, Number Theory (math.NT), Barnes gamma function, Gamma, beta and polygamma functions, 11M35, 35B15
multiple Hurwitz-Lerch zeta function, Raabe type formula, Mathematics - Number Theory, FOS: Mathematics, Jackson integral, Hurwitz and Lerch zeta functions, Number Theory (math.NT), Barnes gamma function, Gamma, beta and polygamma functions, 11M35, 35B15
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