On the zeros of a class of polynomials including the generalized Bessel polynomials
type: Item
instance of: scholarly article
title: On the zeros of a class of polynomials including the generalized Bessel polynomials
zbMATH Open document ID: 0797.26011
DOI: 10.1016/0377-0427(93)90140-7
published in: Journal of Computational and Applied Mathematics
publication date: 1994-10-13T00:00:00Z
review text: Using the tridiagonal background of the defining equations for the polynomials \[ a_{n+1} P_{n+1}(x)- a_ n P_{n-1}(x)- b_ n P_ n(x)= c_ n xP_ n(x);\;P_ 0(x)=0,\;P_ 1(x)= 1, \] (called `a finite Hilbert-space setting' by the authors) a very short and elegant proof is given of the main result: if \(b_ n>0\), \(a_ n\neq 0\), \(c_ n>0\) then every zero of \(P_ n\) has negative real part. Applications to the situation of associated Bessel polynomials (\(a_ n=1;\;b_ n=\delta_{n,1};\;c_ n=2(n+\nu)\)-including the Bessel polynomials for \(\nu= 1/2\)) and the generalized Bessel polynomials are given, reproving and (partially) improving known results. Also bounds for the (negative) real parts of the zeros are given.
Mathematics Subject Classification ID: 26C10
Mathematics Subject Classification ID: 33C10
Mathematics Subject Classification ID: 15A18
zbMATH DE Number: 540454
zbMATH Keywords: zeros
zbMATH Keywords: polynomials
zbMATH Keywords: associated Bessel polynomials
zbMATH Keywords: generalized Bessel polynomials
author: E. K. Ifantis
author: Panayiotis D. Siafarikas
reviewed by: Marcel G. de Bruin
MaRDI profile type: Publication
full work available at URL: 0377-0427(93)90140-7
OpenAlex ID: W1978867346
cites work: Remarks on the Bessel Polynomials
cites work: Q3919971
cites work: A New Class of Orthogonal Polynomials: The Bessel Polynomials
cites work: On the Zeros of a Confluent Hypergeometric Function
cites work: Remarks on the Zeros of Bessel Polynomials
description: scientific article; zbMATH DE number 540454