Deformed Mittag-Leffler Polynomials

TL;DR

This paper introduces deformed Mittag-Leffler polynomials using generalized powers and deformed exponentials, exploring their properties, zeros, and related real polynomials with real zeros.

Contribution

It presents a new class of deformed Mittag-Leffler polynomials, analyzing their recurrence, differential properties, and orthogonality, along with associated real-zero polynomials.

Findings

Polynomials have all zeros on the imaginary axis.

Derived recurrence relations and differential properties.

Established orthogonality of the polynomials.

Abstract

The starting point of this paper are the Mittag-Leffler polynomials introduced by H. Bateman [1]. Based on generalized integer powers of real numbers and deformed exponential function, we introduce deformed Mittag-Leffler polynomials defined by appropriate generating function. We investigate their recurrence relations, differential properties and orthogonality. Since they have all zeros on imaginary axes, we also consider real polynomials with real zeros associated to them.