Abstract. In this paper, we define a new class of almost orthogonal polynomials which can be used successfully for modelling of electronic systems which generate orthonormal basis. Especially, for the classical weight function, they can be considered like a generalization of the classical orthogonal polynomials (Legendre, Laguerre, Hermite, . . . ). They are very suitable for analysis and synthesis of imperfect technical systems which are projected to generate orthogonal polynomials, but in the reality generate almost orthogonal polynomials.
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
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