Twisted (h, q)-Bernoulli numbers and polynomials related to twisted (h,q)-zeta function and L-function

Simsek Y.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol.324, no.2, pp.790-804, 2006 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 324 Issue: 2
  • Publication Date: 2006
  • Doi Number: 10.1016/j.jmaa.2005.12.057
  • Journal Name: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.790-804
  • Keywords: q-Bernoulli numbers and polynomials, twisted q-Bernoulli numbers and polynomials, q-zeta function, L-function, twisted q-zeta function, twisted q-L-functions, q-Volkenborn integral, Q-ZETA FUNCTIONS, Q-ANALOG, SERIES
  • Akdeniz University Affiliated: Yes

Abstract

In this paper, by using q-Volkenborn integral, we construct new generating functions of the new twisted (h, q)-Bernoulli polynomials and numbers. By applying the Mellin transformation to these generating functions, we obtain integral representations of the new twisted (h, q)-zeta function and twisted (h, q)-L-function, which interpolate the twisted (h, q)-Bernoulli numbers and generalized twisted (h, q)-Bemoulli numbers at non-positive integers, respectively. Furthermore, relation between twisted (h, q)-zeta function and twisted (h, q)-L-function are proved. Some new relations, related to twisted (h, q)-Bemoulli polynomials and numbers, are given. (c) 2005 Elsevier Inc. All rights reserved.