MMN-2587

On two bivariate kinds of (p, q)-Bernoulli polynomials

P. Njionou Sadjang; Ugur Duran;

Abstract

The main aim of this paper is to introduce and investigate $(p,q)$-extensions of two bivariate kinds of Bernoulli polynomials and numbers. We firstly examine several $(p,q)$-analogues of the Taylor expansions of products of some trigonometric functions and determine their coefficients which are also analyzed in detail. Then, we introduce two bivariate kinds of $(p,q)$-Bernoulli polynomials and acquired multifarious formulas and relations including connection formulas, recurrence formulas, correlations with aforementioned coefficients, partial $(p,q)$-differential equations and $(p,q)$-integral representations.


Vol. 20 (2019), No. 2, pp. 1185-1199
DOI: https://doi.org/10.18514/MMN.2019.2587


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