Duran, U.; Acikgoz, M. Modified degenerate Carlitz's q-bernoulli polynomials and numbers with weight (α,β). Int. J. Nonlinear Anal. Appl. 2017, 8, 135–144.
Duran, U.; Acikgoz, M. Modified degenerate Carlitz's q-bernoulli polynomials and numbers with weight (α,β). Int. J. Nonlinear Anal. Appl. 2017, 8, 135–144.
Duran, U.; Acikgoz, M. Modified degenerate Carlitz's q-bernoulli polynomials and numbers with weight (α,β). Int. J. Nonlinear Anal. Appl. 2017, 8, 135–144.
Duran, U.; Acikgoz, M. Modified degenerate Carlitz's q-bernoulli polynomials and numbers with weight (α,β). Int. J. Nonlinear Anal. Appl. 2017, 8, 135–144.
Abstract
The main goal of the present paper is to construct some families of the Carlitz’s q-Bernoulli polynomials and numbers. We firstly introduce the modified Carlitz’s q-Bernoulli polynomials and numbers with weight (α, β) and investigate their some explicit properties and identities arising from the bosonic q-Volkenborn integral on ℤp. We then define the modified degenerate Carlitz’s q-Bernoulli polynomials and numbers with weight (α, β) and obtain some recurrence relations and other identities. Moreover, we derive some correlations with the modified Carlitz’s q-Bernoulli polynomials with weight (α, β), the modified degenerate Carlitz’s q-Bernoulli polynomials with weight (α, β), the Stirling numbers of the first kind and second kind.
Keywords
Carlitz’s q-Bernoulli polynomials; Stirling numbers of the first kind; Stirling numbers of the second kind; p-adic q-integral
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
