Journal article
A generic polynomial solution for the differential equation of hypergeometric type and six sequences of orthogonal polynomials related to it
Publication Details
Authors: | Koepf, W.; Masjed-Jamei, M. |
Publication year: | 2006 |
Journal: | Integral Transforms and Special Functions |
Pages range : | 559-576 |
Volume number: | 17 |
Start page: | 559 |
End page: | 576 |
ISSN: | 1065-2469 |
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.
