On $q$-hypergeometric Bernoulli polynomials and numbers

Authors : Salifou MBOUTNGAM, Patrick NJIONOU SADJANG

Pages : 1251-1267

Doi:10.15672/hujms.669940

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Publication Date : 2021-10-15

Article Type : Research Paper

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