Nonlinear characterizations for functions of hypergeometric type and their derivatives of any order
type: Item
instance of: scholarly article
title: Nonlinear characterizations for functions of hypergeometric type and their derivatives of any order
zbMATH Open document ID: 0803.33009
author: A. Sarsa
author: Jesús S. Dehesa
author: R. J. Yáñez
author: Manuel Pérez-Victoria
published in: Journal of Mathematical Analysis and Applications
publication date: 1994-08-17T00:00:00Z
review text: The so-called functions of hypergeometric type \(y\equiv y_ \nu(x)\) are solutions of the differential equation \(\sigma (z)y''+ \tau(z) y'+ \lambda y=0\), where \(\sigma\), \(\tau\) and \(\lambda\) are polynomials of degrees, at most 2, 1 and 0, respectively, and \(\nu\) is a root of the equation \(\lambda+ \nu\tau'+ {1\over 2} \nu(\nu -1) \sigma''=0\). The authors establish two interesting characterizations for these functions and their derivatives. Each characterization consists of four different quadratic differential-difference equations among \(y_ \nu^{(k)} (z)\). Applications to the hypergeometric type polynomials are shown. In particular, the coefficients of the relationships are explicitly given for the classical orthogonal polynomials of Jacobi, Laguerre, Hermite and Bessel.
reviewed by: Luigi Gatteschi
Mathematics Subject Classification ID: 33C45
zbMATH DE Number: 617439
zbMATH Keywords: functions of hypergeometric type
MaRDI profile type: Publication
full work available at URL: jmaa.1994.1181
OpenAlex ID: W2042060829
Wikidata QID: Q58363545
DOI: 10.1006/JMAA.1994.1181
description: scientific article; zbMATH DE number 617439