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Modified Clebsch-Gordan-type expansions for products of discrete hypergeometric polynomials

Opened Access Modified Clebsch-Gordan-type expansions for products of discrete hypergeometric polynomials

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Autor: Álvarez Nodarse, Renato
Yáñez García, Rafael José
Sánchez Dehesa, Jesús
Departamento: Universidad de Sevilla. Departamento de Análisis Matemático
Fecha: 1998-03-09
Publicado en: Journal of Computational and Applied Mathematics, 89 (1), 171-197.
Tipo de documento: Artículo
Resumen: Starting from the second-order difference hypergeometric equation satisfied by the set of discrete orthogonal polynomials ∗pn∗, we find the analytical expressions of the expansion coefficients of any polynomial rm(x) and of the product rm(x)qj(x) in series of the set ∗pn∗. These coefficients are given in terms of the polynomial coefficients of the second-order difference equations satisfied by the involved discrete hypergeometric polynomials. Here qj(x) denotes an arbitrary discrete hypergeometric polynomial of degree j. The particular cases in which ∗rm∗ corresponds to the non-orthogonal families ∗xm∗, the rising factorials or Pochhammer polynomials ∗(x)m∗ and the falling factorial or Stirling polynomials ∗x[m]∗ are considered in detail. The connection problem between discrete hypergeometric polynomials, which here corresponds to the product case with m = 0, is also studied and its complete solution for all the classical discrete orthogonal hypergeometric (CDOH) polynomials is given....
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Cita: Álvarez Nodarse, R., Yáñez García, R.J. y Sánchez Dehesa, J. (1998). Modified Clebsch-Gordan-type expansions for products of discrete hypergeometric polynomials. Journal of Computational and Applied Mathematics, 89 (1), 171-197.
Tamaño: 327.9Kb
Formato: PDF

URI: http://hdl.handle.net/11441/42997

DOI: 10.1016/S0377-0427(97)00244-6

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