On generalized q-poly-Bernoulli numbers and polynomials

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Bilgic S., Kurt V.

Filomat, vol.34, no.2, pp.515-520, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 34 Issue: 2
  • Publication Date: 2020
  • Doi Number: 10.2298/fil2002515b
  • Journal Name: Filomat
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Page Numbers: pp.515-520
  • Keywords: ernoulli numbers and polynomials, Euler numbers and polynomials, q-Bernoulli polinomials, q-Euler polynomials, Polylogarithm function, Stirling numbers of the second kind, poly-Bernoulli polynomials, poly-Genocchi polynomials, EULER
  • Anadolu University Affiliated: No

Abstract

© 2020, University of Nis. All rights reserved.Many mathematicians in ([1], [2], [5], [14], [20]) introduced and investigated the generalized q-Bernoulli numbers and polynomials and the generalized q-Euler numbers and polynomials and the generalized q-Gennochi numbers and polynomials. Mahmudov ([15], [16]) considered and investigated the q-Bernoulli polynomials B(α) n,q x, y in x, y of order α and the q-Euler polynomials E(α) n,q x, y in x, y of order α. In this work, we define generalized q-poly-Bernoulli polynomials B[k,α] n,q x, y in x, y of order α. We give new relations between the generalized q-poly-Bernoulli polynomials B[k,α] n,q x, y in x, y of order α and the generalized q-poly-Euler polynomials E[k,α] n,q x, y in x, y of order α and the q-Stirling numbers of the second kind S2,q (n,k).