Preprint Article Version 1 This version not peer reviewed

Modified Degenerate Carlitz’s q-Bernoulli Polynomials and Numbers with Weight (α, β)

Version 1 : Received: 14 December 2017 / Approved: 15 December 2017 / Online: 15 December 2017 (09:31:13 CET)

A peer-reviewed article of this Preprint also exists.

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.

Journal reference: The International Journal of Nonlinear Analysis and Applications (IJNAA) 2017, 8, 135-144
DOI: 10.22075/ijnaa.2017.11767.1588

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.

Subject Areas

Carlitz’s q-Bernoulli polynomials; Stirling numbers of the first kind; Stirling numbers of the second kind; p-adic q-integral

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