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Generating functions of orthogonal polynomials and Szegö-Jacobi parameters

Asai N., Kubo I., Kuo H.-H.

Probability and Mathematical Statistics

2003

Vol. 23, Fasc. 2

273--291

In this paper, we present a more direct way to compute the Szegö-Jacobi parameters from a generating function than that in [5] and [6]. Our study is motivated by the notions of one-mode interacting Fock spaces defined in[1] and Segal-Bargmann transform associated with non-Gaussian probability measures introduced in [2]. Moreover, we examine the relationships between the representations of orthogonal polynomials in terms of differential or difference operators and our generating functions. The connections provide practical criteria to determine when functions of a certain form are orthogonal polynomials.