On (i, q) Bernoulli and Euler numbers

CENKCİ M., Kurt V., Rim S. H., ŞİMŞEK Y.

APPLIED MATHEMATICS LETTERS, vol.21, no.7, pp.706-711, 2008 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 21 Issue: 7
  • Publication Date: 2008
  • Doi Number: 10.1016/j.aml.2007.08.001
  • Journal Name: APPLIED MATHEMATICS LETTERS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.706-711
  • Keywords: Bernoulli and Euler numbers, p-adic q-integral, INTEGRALS
  • Akdeniz University Affiliated: Yes

Abstract

The p-adic invariant q-integral on Z(p) was originally constructed by T. Kim [T. Kim, On a q-analogue of the p-adic log gamma function and related integrals, J. Number Theory 76 (1999) 320-329]. Recently, many authors have been studying the extended Bernoulli numbers or Euler numbers by using this p-adic q-integral in the fermionic or bosonic sense. Let i epsilon 0(Cp) = {x epsilon C-p : vertical bar x vertical bar(p) <= 1} Then we consider new (i, q)-Bernoulli and Euler numbers using p-adic q-integrals in this work. (C) 2007 Elsevier Ltd. All rights reserved.