Ryoo, Cheon Seoung; Kim, Taekyun An analogue of the zeta function and its applications. (English) Zbl 1112.11013 Appl. Math. Lett. 19, No. 10, 1068-1072 (2006). Summary: We construct new analogues of Bernoulli numbers and polynomials. We define the \(q\)-extension of zeta function. Finally we give relation between the \(q\)-extension of zeta functions and the \((h,q)\)-extension of Bernoulli polynomials. Cited in 1 ReviewCited in 5 Documents MSC: 11B68 Bernoulli and Euler numbers and polynomials 11S40 Zeta functions and \(L\)-functions 33B30 Higher logarithm functions 33D15 Basic hypergeometric functions in one variable, \({}_r\phi_s\) Keywords:Bernoulli numbers and polynomials; \(q\)-Bernoulli numbers and polynomials; zeta functions PDF BibTeX XML Cite \textit{C. S. Ryoo} and \textit{T. Kim}, Appl. Math. Lett. 19, No. 10, 1068--1072 (2006; Zbl 1112.11013) Full Text: DOI References: [1] Kim, T., Analytic continuation of multiple \(q\)-zeta functions and their values at negative integers, Russ. J. math. phys, 11, 71-76, (2004) · Zbl 1115.11068 [2] Kim, T., Non-Archimedean \(q\)-integrals associated with multiple changhee \(q\)-Bernoulli polynomials, Russ. J. math. phys., 10, 91-98, (2003) · Zbl 1072.11090 [3] Kim, T., \(q\)-volkenborn integration, Russ. J. math. phys., 9, 288-299, (2002) · Zbl 1092.11045 [4] Kim, T., \(q\)-Riemann zeta functions, Int. J. math. math. sci., 2004, 12, 599-605, (2004) · Zbl 1122.11082 [5] Kim, T.; Rim, S.H., Generalized carlitz’s \(q\)-Bernoulli numbers in the \(p\)-adic number field, Adv. stud. contemp. math., 2, 9-19, (2000) · Zbl 1050.11020 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.