On the analogs of bernoulli and euler numbers, related identities and zeta and L-functions

Creative Commons License

Kim T., Rim S., ŞİMŞEK Y., Kim D.

JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, vol.45, no.2, pp.435-453, 2008 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 45 Issue: 2
  • Publication Date: 2008
  • Doi Number: 10.4134/jkms.2008.45.2.435
  • Journal Name: JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.435-453
  • Keywords: Bernoulli numbers and polynomials, zeta functions
  • Akdeniz University Affiliated: Yes

Abstract

In this paper, by using q-deformed bosonic p-adic integral, we give lambda-Bernoulli numbers and polynomials, we prove Witt's type formula of lambda-Bernoulli polynomials and Gauss multiplicative formula for lambda-Bernoulli polynomials. By using derivative operator to the generating functions of lambda-Bernoulli polynomials and generalized lambda-Bernoulli numbers, we give Hurwitz type lambda-zeta functions and Dirichlet's type lambda-Lfunctions; which are interpolated lambda-Bernoulli polynomials and generalized lambda-Bernoulli numbers, respectively. We give generating function of lambda-Bernoulli numbers with order r. By using Mellin transforms to their function, we prove relations between multiply zeta function and lambda-Bernoulli polynomials and ordinary Bernoulli numbers of order r and lambda-Bernoulli numbers, respectively. We also study on lambda-Bernoulli numbers and polynomials in the space of locally constant. Moreover, we define A-partial zeta function and interpolation function.