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The deformed and modified Mittag-Leffler polynomials. (English) Zbl 1225.33028
Summary: The starting point of this paper are the Mittag-Leffler polynomials investigated in details by H. Bateman [Proc. Natl. Acad. Sci. USA 26, 491–496 (1940; Zbl 0061.14106; JFM 66.0325.02)]. Based on generalized integer powers of real numbers and deformed exponential functions, we introduce deformed Mittag-Leffler polynomials defined by the appropriate generating function. We investigate their recurrence relations, hypergeometric representation and orthogonality. Since they have all zeros on the imaginary axes, we also consider real polynomials with real zeros associated to them.
33E12Mittag-Leffler functions and generalizations
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