On $q$-hypergeometric Bernoulli polynomials and numbers

Year 2021, Volume: 50 Issue: 5, 1251 - 1267, 15.10.2021

Salifou Mboutngam Patrick Njıonou Sadjang

https://doi.org/10.15672/hujms.669940

Abstract

We introduce $q$-analogues of the hypergeometric Bernoulli polynomials in one and two real parameters and study several of their properties. Also we provide the inversion, the power representation, the multiplication and the addition formula for these polynomials. Classical results are recovered by limit transition.

Keywords

$q$-Bernoulli polynomials, $q$-Bernoulli numbers, $q$-hypergeometric Bernoulli polynomials, recurrence relation, $q$-difference equation

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