Inversion problems in the \(q\)-Hahn tableau
type: Item
instance of: scholarly article
title: Inversion problems in the \(q\)-Hahn tableau
zbMATH Open document ID: 0953.33005
author: A. Zarzo
author: Iván Area
author: Eduardo Godoy
author: A. Ronveaux
published in: Journal of Symbolic Computation
publication date: 2001-01-23T00:00:00Z
review text: If \(\{P_n(x;q)\}\) is a family of polynomials belonging to the \(q-\)Hahn tableau (see \textit{T. H. Koornwinder} [Pitman Res. Notes Math. Ser. 311, 46-128 (1994; Zbl 0821.17015)]) then each polynomial of this family can be written as \(P_n(x;q)=\sum_{m=0}^n D_m(n)\vartheta_m(x)\) where \(\vartheta_m(x)\) stands for \((x;q)_m\) or \(x^m\). In this paper the corresponding inversion problem is solved, that is, the explicit expression is found for the coefficients \(I_m(n)\) in the expansion \(\vartheta_m(x)=\sum_{m=0}^n I_m(n) P_m(x;q)\). The algorithm, called Navima, can be obtained from \url{http://www.uvigo.es/webs/t10/navima}.
Mathematics Subject Classification ID: 33C47
Mathematics Subject Classification ID: 33F10
zbMATH DE Number: 1423189
zbMATH Keywords: orthogonal polynomials
zbMATH Keywords: inversion problems
zbMATH Keywords: \(q\)-Hahn tableau
reviewed by: Nico M. Temme
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1423189