Convolution Theorem for (<i>p</i>,<i>q</i>)-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

• <i>q</i>-derivative
• (<i>p</i>,<i>q</i>)-convolution theorem
• (<i>p</i>,<i>q</i>)-trigonometric functions
• (<i>p</i>,<i>q</i>)-exponential functions
• (<i>p</i>,<i>q</i>)-differential operators