The deformed and modified Mittag-Leffler polynomials

The starting point of this paper are the Mittag–Leffler polynomials investigated in details 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, hypergeometric representation 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