ON THE ANALOGS OF BERNOULLI AND EULER NUMBERS, RELATED IDENTITIES AND ZETA AND L-FUNCTIONS

- Journal title : Journal of the Korean Mathematical Society
- Volume 45, Issue 2, 2008, pp.435-453
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/JKMS.2008.45.2.435

Title & Authors

ON THE ANALOGS OF BERNOULLI AND EULER NUMBERS, RELATED IDENTITIES AND ZETA AND L-FUNCTIONS

Kim, Tae-Kyun; Rim, Seog-Hoon; Simsek, Yilmaz; Kim, Dae-Yeoul;

Kim, Tae-Kyun; Rim, Seog-Hoon; Simsek, Yilmaz; Kim, Dae-Yeoul;

Abstract

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

Keywords

Bernoulli numbers and polynomials;zeta functions;

Language

English

Cited by

1.

q-Analogues of some results for the Apostol-Euler polynomials,;

Advanced Studies in Contemporary Mathematics, 2010. vol.20. 1, pp.103-113

2.

Unification of Multiple Lerch-Zeta Type Functions,;;

Advanced Studies in Contemporary Mathematics, 2011. vol.21. 4, pp.367-374

3.

INTERPOLATION FUNCTIONS OF THE EULERIAN TYPE POLYNOMIALS AND NUMBERS,;

Advanced Studies in Contemporary Mathematics, 2013. vol.23. 2, pp.301-307

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