Convolution Theorem for (p,q)-Gamma Integral Transforms and Their Application to Some Special Functions

Abstract

This article introduces (𝑝,𝑞)-analogs of the gamma integral operator and discusses their expansion to power functions, (𝑝,𝑞)-exponential functions, and (𝑝,𝑞)-trigonometric functions. Additionally, it validates other findings concerning (𝑝,𝑞)-analogs of the gamma integrals to unit step functions as well as first- and second-order (𝑝,𝑞)-differential operators. In addition, it presents a pair of (𝑝,𝑞)-convolution products for the specified (𝑝,𝑞)-analogs and establishes two (𝑝,𝑞)-convolution theorems.

Keywords: Q-Derivative; (P,Q)-Convolution, Theorem; (P,Q)-Trigonometric Functions, (P,Q)-Exponential Functions, (P,Q)-Differential Operators