Preprint
A generic polynomial solution for the differential equation of hypergeometric type and six sequences of orthogonal polynomials related to it
Abstract
In this work, we present a generic formula for the polynomial solution families of the well-known differential equation of hypergeometric type s(x)y"n(x) + t(x)y'n(x) - lnyn(x) = 0 and show that all the three classical orthogonal polynomial families as well as three finite orthogonal polynomial families, extracted from this equation, can be identified as special cases of this derived polynomial sequence. Some general properties of this sequence are also given.
Citation
@article{urn:nbn:de:hebis:34-200604048989,
author={Koepf, Wolfram and Masjed-Jamei, Mohammad},
title={A generic polynomial solution for the differential equation of hypergeometric type and six sequences of orthogonal polynomials related to it},
year={2005}
}
0500 Oax 0501 Text $btxt$2rdacontent 0502 Computermedien $bc$2rdacarrier 1100 2005$n2005 1500 1/eng 2050 ##0##urn:nbn:de:hebis:34-200604048989 3000 Koepf, Wolfram 3010 Masjed-Jamei, Mohammad 4000 A generic polynomial solution for the differential equation of hypergeometric type and six sequences of orthogonal polynomials related to it / Koepf, Wolfram 4030 4060 Online-Ressource 4085 ##0##=u http://nbn-resolving.de/urn:nbn:de:hebis:34-200604048989=x R 4204 \$dPreprint 4170 Mathematische Schriften Kassel 7136 ##0##urn:nbn:de:hebis:34-200604048989
2006-04-04T11:47:41Z 2006-04-04T11:47:41Z 2005 urn:nbn:de:hebis:34-200604048989 http://hdl.handle.net/123456789/200604048989 157436 bytes application/pdf eng Urheberrechtlich geschützt https://rightsstatements.org/page/InC/1.0/ Klassische orthogonale Polynome Hypergeometrische Differentialgleichung Differential equation of hypergeometric type Weight function Hypergeometric functions Hypergeometric identities Recurrence equations 510 A generic polynomial solution for the differential equation of hypergeometric type and six sequences of orthogonal polynomials related to it Preprint In this work, we present a generic formula for the polynomial solution families of the well-known differential equation of hypergeometric type s(x)y"n(x) + t(x)y'n(x) - lnyn(x) = 0 and show that all the three classical orthogonal polynomial families as well as three finite orthogonal polynomial families, extracted from this equation, can be identified as special cases of this derived polynomial sequence. Some general properties of this sequence are also given. open access Koepf, Wolfram Masjed-Jamei, Mohammad Mathematische Schriften Kassel 05, 15 33C45 33C20 33F10 Mathematische Schriften Kassel 05, 15
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