Hacettepe Journal of Mathematics and Statistics 2651-477X 2651-477X Hacettepe University 10.15672/hujms.669940 Mathematical Sciences Matematik On $q$-hypergeometric Bernoulli polynomials and numbers https://orcid.org/0000-0002-4560-0961 Mboutngam Salifou University of Maroua, Higher Teacher Training College https://orcid.org/0000-0002-5196-6855 Njıonou Sadjang Patrick University of Douala, Faculty of Industrial Engineering 10 15 2021 50 5 1251 1267 01 04 2020 03 21 2021 Copyright © 2002, Hacettepe Journal of Mathematics and Statistics 2002 Hacettepe Journal of Mathematics and Statistics

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.

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