Work

A Two-Way Convolution of the Mittag-Leffler Function with Sheffer Polynomials

Year: 2026

Type: article

Abstract: This article presents a two-way convolution of the Mittag-Leffler function with Sheffer polynomials via the umbral algebraic method, thereby introducing the Mittag-Leffler–Sheffer polynomials (MLSPs) and the Sheffer–Mittag-Leffler function (SMLF). We establish their generating functions, series definitions, quasi-monomial properties, and differential equations. Using Wronskian and Pascal functional matrices, we derive recursive formulas and differential recursive identities for these hybrid polynomials. Various special cases including Mittag-Leffler–Appell, Mittag-Leffler–Hermite, and Mittag-Leffler–Miller–Lee polynomials are examined. Additionally, a graphical investigation of the zero distributions of selected members of these polynomial families is presented using computational tools.

Source: Mathematics

DOI: 10.3390/math14173093

Authors: Waseem Ahmad Khan, Areefa Khatoon, Khidir Shaib Mohamed, Muntasir Suhail, Habeeb Ibrahim, Naglaa Mohammed

Institutions: Prince Mohammad bin Fahd University, Symbiosis International University, Qassim University

Language: English

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: Qassim University