Aufsatz in einer Fachzeitschrift
A generic polynomial solution for the differential equation of hypergeometric type and six sequences of orthogonal polynomials related to it
Details zur Publikation
Autor(inn)en: | Koepf, W.; Masjed-Jamei, M. |
Publikationsjahr: | 2006 |
Zeitschrift: | Integral Transforms and Special Functions |
Seitenbereich: | 559-576 |
Jahrgang/Band : | 17 |
Erste Seite: | 559 |
Letzte Seite: | 576 |
ISSN: | 1065-2469 |
Zusammenfassung, Abstract
In this work, we present a generic formula for the polynomial solution families of the well-known differential equation of hypergeometric type sigma(x) y(n)''(x)+tau(x)y(n)'(x)-lambda(n)y(n)(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.
In this work, we present a generic formula for the polynomial solution families of the well-known differential equation of hypergeometric type sigma(x) y(n)''(x)+tau(x)y(n)'(x)-lambda(n)y(n)(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.
