On Two Bivariate Kinds of (p,q)-Bernoulli Polynomials

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.