Abstract
In this paper, we introduce and study the new family of analytic functions via Rodrigues formula. Some main properties, the generating function, various recurrence relations and differential properties of these functions are obtained. Furthermore, the differential equations are given for the subclasses of this family of analytic functions.
Highlights
Multiple orthogonal polynomials which are extensions of the orthogonal polynomials have been an important research area during the last few decades
We introduce and study a new family of analytic functions via Rodrigues formula
The Rodrigues type generalizations of the multiple orthogonal polynomials have been studied in the papers [12] and [16]
Summary
Multiple orthogonal polynomials which are extensions of the orthogonal polynomials have been an important research area during the last few decades (see [6], [7], [8], [10], [11], [14]) These polynomials are closely related to Hermite-Padé approximation of a system of Markov functions [15]. The multiple orthogonal polynomials appear in random matrix theory, number theory, probability, approximation theory and mathematical physics (for examples see [1], [5], [9], [13], [15], [17]) These polynomials have some general properties such as Rodrigues formula and generating function. Multiple Hermite polynomials, Rodrigues formula, generating function, recurrence relation, di¤erential equation.
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