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