Stieltjes functions and discrete classical orthogonal polynomials

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Data

2013-10-01

Autores

Bracciali, Cleonice Fátima [UNESP]
Perez, Teresa E.
Pinar, Miguel A.

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Editor

Springer

Resumo

Classical orthogonal polynomials can be characterized in terms of the corresponding Stieltjes function. We consider the construction of a Stieltjes function in terms of the falling factorials for discrete classical orthogonal polynomials (Charlier, Krawtchouk, Meixner, and Hahn). This Stieltjes function associated with classical orthogonal polynomials of a discrete variable is solution of a non-homogeneous difference equation. That property characterizes the discrete classical measures. In addition, an hypergeometric expression for the Stieltjes function is obtained in all the discrete classical cases.

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Palavras-chave

Difference equations, Stieltjes functions, Classical orthogonal polynomials of a discrete variable

Como citar

Computational & Applied Mathematics. Heidelberg: Springer Heidelberg, v. 32, n. 3, p. 537-547, 2013.