A Study of the <i>q</i>-Truncated Exponential–Appell Polynomials

Abstract

This article introduces the 2-variable q-truncated exponential–Appell (q-trunc. exp. Appell) polynomials and investigates their fundamental properties. Specific results are derived for the q-trunc. exp. Appell family along with their graphical representations which contribute to advancing the understanding of q-series and q-special functions. Potential applications of these polynomials span various disciplines, including combinatorics (such as partition theory and combinatorial identities), number theory (such as q-analogues of classical number-theoretic functions), and mathematical physics (such as in quantum groups and statistical mechanics). This study concludes with the introduction of the 2-variable q-trunc. exp. λ-polynomials, thereby broadening the scope and relevance of this research.

Keywords

• <i>q</i>-truncated exponential polynomials
• <i>q</i>-Appell polynomials
• <i>q</i>-recurrence relations
• determinant forms
• extended quasi-monomiality