Preprint
Orthogonal polynomials and recurrence equations, operator equations and factorization
Abstract
This article surveys the classical orthogonal polynomial systems of the Hahn class, which are solutions of second-order differential, difference or q-difference equations. Orthogonal families satisfy three-term recurrence equations. Example applications of an algorithm to determine whether a three-term recurrence equation has solutions in the Hahn class - implemented in the computer algebra system Maple - are given. Modifications of these families, in particular associated orthogonal systems, satisfy fourth-order operator equations. A factorization of these equations leads to a solution basis.
Citation
@article{urn:nbn:de:hebis:34-200604069128,
author={Koepf, Wolfram},
title={Orthogonal polynomials and recurrence equations, operator equations and factorization},
year={2005}
}
0500 Oax 0501 Text $btxt$2rdacontent 0502 Computermedien $bc$2rdacarrier 1100 2005$n2005 1500 1/eng 2050 ##0##urn:nbn:de:hebis:34-200604069128 3000 Koepf, Wolfram 4000 Orthogonal polynomials and recurrence equations, operator equations and factorization / Koepf, Wolfram 4030 4060 Online-Ressource 4085 ##0##=u http://nbn-resolving.de/urn:nbn:de:hebis:34-200604069128=x R 4204 \$dPreprint 4170 Mathematische Schriften Kassel 7136 ##0##urn:nbn:de:hebis:34-200604069128
2006-04-06T14:17:34Z 2006-04-06T14:17:34Z 2005 urn:nbn:de:hebis:34-200604069128 http://hdl.handle.net/123456789/200604069128 168454 bytes application/pdf eng Universität Kassel, FB 17, Mathematik/Informatik Urheberrechtlich geschützt https://rightsstatements.org/page/InC/1.0/ Orthogonale Polynome Differentialgleichung Differenzengleichung Hypergeometrische Reihe Maple <Programm> Computer Algebra Hahn Class Orthogonal polynomials Differential equations Q-difference equations Hypergeometric functions Factorization of operator polynomials 510 Orthogonal polynomials and recurrence equations, operator equations and factorization Preprint This article surveys the classical orthogonal polynomial systems of the Hahn class, which are solutions of second-order differential, difference or q-difference equations. Orthogonal families satisfy three-term recurrence equations. Example applications of an algorithm to determine whether a three-term recurrence equation has solutions in the Hahn class - implemented in the computer algebra system Maple - are given. Modifications of these families, in particular associated orthogonal systems, satisfy fourth-order operator equations. A factorization of these equations leads to a solution basis. open access Koepf, Wolfram Mathematische Schriften Kassel 05, 14 39A70 33D15 33D45 33C20 33C45 Mathematische Schriften Kassel 05, 14
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