Truncated-Exponential-Based General-Appell Polynomials

Zeynep Özat (), Bayram Çekim, Mehmet Ali Özarslan and Francesco Aldo Costabile
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Zeynep Özat: Graduate School of Natural and Applied Sciences, Gazi University, Ankara 06500, Türkiye
Bayram Çekim: Department of Mathematics, Faculty of of Science, Gazi University, Ankara 06560, Türkiye
Mehmet Ali Özarslan: Department of Mathematics, Faculty of Arts and Sciences, Eastern Mediterranean University, North Cyprus, via Mersin 10, Famagusta 99628, Türkiye
Francesco Aldo Costabile: Department of Mathematics and Computer Science, University of Calabria, 87036 Rende, CS, Italy

Mathematics, 2025, vol. 13, issue 8, 1-15

Abstract: In this paper, a new and general form of truncated-exponential-based general-Appell polynomials is introduced using the two-variable general-Appell polynomials. For this new polynomial family, we present an explicit representation, recurrence relation, shift operators, differential equation, determinant representation, and some other properties. Finally, two special cases of this family, truncated-exponential-based Hermite-type and truncated-exponential-based Laguerre–Frobenius Euler polynomials, are introduced and their corresponding properties are obtained.

Keywords: Appell polynomials; bivariate Appell polynomials; truncated exponential polynomials (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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