New Summation and Integral Representations for 2-Variable (p,q)-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.

Two-Variable q-Hermite-Based Appell Polynomials and Their Applications

“…In certain cases, we additionally reference published findings. (Check, over the instance [6,8,9,[36][37][38][39][40][41]).…”

“…Multiple researchers have recently investigated and studied a few strange polynomials connected by q-calculus. (See for example [2][3][4][5][6][7][8][9][10]).…”

On q-Hermite Polynomials with Three Variables: Recurrence Relations, q-Differential Equations, Summation and Operational Formulas

“…The q-Hermite polynomials serve a purpose in various fields of mathematics and science, such as non-commutative probability, quantum physics and combinatorics. The concept of q-Hermite polynomials arose from the interest of many academics in the q analogue of these polynomials; we also refer to published findings in particular occurrences (see, for example, [25][26][27][28][29][30][31][32][33] and any mentions within).…”