Tomita, Yoshinobu Hermite’s formulas for \(q\)-analogues of Hurwitz zeta functions. (English) Zbl 1268.11128 Funct. Approximatio, Comment. Math. 45, No. 2, 289-301 (2011). Summary: We treat Hermite’s formulas for \(q\)-analogues of the Hurwitz zeta function. As their application, we study the classical limit of modified \(q\)-analogues of the Hurwitz zeta function. We also treat \(q\)-analogues of the Milnor multiple gamma function. Cited in 3 Documents MSC: 11M35 Hurwitz and Lerch zeta functions 11M41 Other Dirichlet series and zeta functions 33D15 Basic hypergeometric functions in one variable, \({}_r\phi_s\) Keywords:Riemann zeta function; Hurwitz zeta function; multiple gamma function; classical limit; \(q\)-series × Cite Format Result Cite Review PDF Full Text: DOI Euclid References: [1] K. A. Broughan, Vanishing of the integral of the Hurwitz zeta function , Bull. Austral. Math. Soc. 65 (2002), no. 1, 121-127. · Zbl 0994.11031 · doi:10.1017/S000497270002013X [2] M. Kaneko, N. Kurokawa and M. Wakayama, A variation of Euler’s approach to values of the Riemann zeta function , Kyushu J. Math. 57 (2003), no. 1, 175-192. · Zbl 1067.11053 · doi:10.2206/kyushujm.57.175 [3] K. Kawagoe, M. Wakayama and Y. Yamasaki, \(q\) -analogues of the Riemann zeta, the Dirichlet \(L\)-functions, and a crystal zeta function, Forum Math. 20 (2008), no. 1, 1-26. · Zbl 1205.11095 · doi:10.1515/FORUM.2008.001 [4] N. Kurokawa, H. Ochiai and M. Wakayama, Milnor’s multiple gamma functions , J. Ramanujan Math. Soc 21 (2006), no. 2, 153-167. · Zbl 1189.11043 [5] N. Kurokawa and M. Wakayama, Period deformations and Raabe’s formulas for generalized gamma and sine functions , Kyushu J. Math. 62 (2008), no. 1, 171-187. · Zbl 1206.11110 · doi:10.2206/kyushujm.62.171 [6] N. Kurokawa and M. Wakayama, On \(q\) -analogues of the Euler constant and Lerch’s limit formula, Proc. Amer. Math. Soc. 132 (2004), no. 4, 935-943. · Zbl 1114.33022 · doi:10.1090/S0002-9939-03-07025-4 [7] N. Kurokawa and M. Wakayama, Gamma and sine functions for Lie groups and period integrals , Indagationes Mathematicae 16 (2005), no. 3-4, 585-607. · Zbl 1168.11321 · doi:10.1016/S0019-3577(05)80041-2 [8] N. N. Lebedev, Special functions and their applications , Dover Publications Inc., New York, 1972. · Zbl 0271.33001 [9] M. Lerch, Dalši studie v oboru Malmsténovskỳch rǎd , Rozpravy Ceské Akad 3 (1894), no. 28, 1-61. [10] G. A. A. Plana, Mem. R. Accad. Torino XXV, no. 9, 403-418, 1820. [11] Y. Tomita, On \(q\)-analogues of multiple gamma functions and multiple sine functions , preprint, 2009. [12] H. Tsumura, On modification of the \(q\) -\(L\)-series and its applications, Nagoya Math. J. 164 (2001), 185-197. · Zbl 1025.11030 [13] K. Ueno and M. Nishizawa, Quantum groups and zeta-functions , In Quantum groups (Karpacz, 1994), 115-126. PWN, Warsaw, 1995. · Zbl 0874.17006 [14] M. Wakayama and Y. Yamasaki, Integral representations of \(q\)-analogues of the Hurwitz zeta function , Monatshefte für Mathematik 149 (2006), no. 2, 141-154. · Zbl 1110.11029 · doi:10.1007/s00605-005-0369-1 [15] E. T. Whittaker and G. N. Watson, A course of modern analysis , Cambridge Mathematical Library. Cambridge University Press, Cambridge, 1996. · Zbl 0951.30002 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.