New Summation and Integral Representations for 2-Variable (<i>p</i>,<i>q</i>)-Hermite Polynomials

Abstract

In this paper, we introduce and study new features for 2-variable (p,q)-Hermite polynomials, such as the (p,q)-diffusion equation, (p,q)-differential formula and integral representations. In addition, we establish some summation models and their (p,q)-derivatives. Certain parting remarks and nontrivial examples are also provided.

Keywords

• (<i>p</i>,<i>q</i>)-calculus
• 2-variable (<i>p</i>,<i>q</i>)-Hermite polynomials
• shift operator for polynomials
• (<i>p</i>,<i>q</i>)-differential equation summation formulas
• integral representations