The deformed and modified Mittag-Leffler polynomials

Abstract

The starting point of this paper are the Mittag-Leffler polynomials introduced by H. Bateman in [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.Mathematics Subject Classification (2010): 33C45, 11B83

Rolling near the tachyon vacuum

“…11 The polynomials are defined by the inner product of L 0 and K 1 eigenfunctions in the unitary representation D + 1 of SL(2, R) (a member of the discrete series of unitary representations [42]). In the JHEP04(2020)104 mathematics literature, they are known as (a modified version of [43]) the Mittag-Leffler polynomials [44]. The coefficients eq.…”

Rolling Near the Tachyon Vacuum

“…They are defined by the inner product of L 0 and K 1 eigenfunctions in the unitary representation D + 1 of SL(2, R) (a member of the discrete series of unitary representations [38]). In the mathematics literature, they are known as (a modified version of [39]) the Mittag-Leffler polynomials [40]. The coefficients (B.2) follow from the identity…”

Mittag–Leffler functions,lpn-balls and geometric pairings

“…We can also generalize the Mittag-Leffler polynomials. Mittag-Leffler polynomials [34,35] g n (y) are the coefficients of the expansion…”

“…We don't know yet if the orthogonality relations of regular Mittag-Leffler polynomials extend in some way to this generalized polynomials into the family of generalized hypergeometric polynomials. These generalized Mittag-Leffler polynomials can be deformed, like the classical ones as in [34].…”