Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2016; 53(4): 1149-1156

Printed July 31, 2016

https://doi.org/10.4134/BKMS.b150583

Copyright © The Korean Mathematical Society.

On degenerate $q$-Bernoulli polynomials

Taekyun Kim

Kwangwoon University

Abstract

In this paper, we introduce the degenerate Carlitz $q$-Bernoulli numbers and polynomials and give some interesting identities and properties of these numbers and polynomials which are derived from the generating functions and $p$-adic integral equations.

Keywords: $q$-Bernoulli polynomial, degenerate Bernoulli polynomials, $q$-Volkenborn integral

MSC numbers: 05A10, 11B68, 11S80, 05A19