A Study of the q -Truncated Exponential–Appell Polynomials

Francesco Aldo Costabile, Subuhi Khan and Hassan Ali ()
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Francesco Aldo Costabile: Department of Mathematics and Computer Science, University of Calabria, 87036 Rende, CS, Italy
Subuhi Khan: Department of Mathematics, Faculty of Science, Aligarh Muslim University, Aligarh 202002, India
Hassan Ali: Department of Mathematics, Faculty of Science, Aligarh Muslim University, Aligarh 202002, India

Mathematics, 2024, vol. 12, issue 23, 1-18

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: q -truncated exponential polynomials; q -Appell polynomials; q -recurrence relations; determinant forms; extended quasi-monomiality (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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