10 papers · 1 filter
Inversion formulas involving orthogonal polynomials and some of their applications
Roelof Koekoek
We derive inversion formulas involving orthogonal polynomials which can be used to find coefficients of differential equations satisfied by certain generalizations of the classical…
The Jacobi inversion formula
J. Koekoek, R. Koekoek
We look for spectral type differential equations satisfied by the generalized Jacobi polynomials which are orthogonal on the interval [-1,1] with respect to a weight function consi…
Finding differential equations for symmetric generalized ultraspherical polynomials by using inversion methods
J. Koekoek, R. Koekoek
We find all spectral type differential equations satisfied by the symmetric generalized ultraspherical polynomials which are orthogonal on the interval [-1,1] with respect to the c…
Inversion methods for finding differential equations for generalized Jacobi polynomials
J. Koekoek, R. Koekoek
We look for differential equations satisfied by the generalized Jacobi polynomials which are orthogonal on the interval [-1,1] with respect to a weight function consisting of the c…
On differential equations for Sobolev-type Laguerre polynomials
J. Koekoek, R. Koekoek, H. Bavinck
We obtain all spectral type differential equations satisfied by the Sobolev-type Laguerre polynomials. This generalizes the results found in 1990 by the first and second author in…
On a difference equation for generalizations of Charlier polynomials
Herman Bavinck, Roelof Koekoek
In this paper we obtain a set of polynomials which are orthogonal with respect to the classical discrete weight function of the Charlier polynomials at which an extra point mass at…