5 papers
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…
A note on the q-derivative operator
J. Koekoek, R. Koekoek
We prove a formula for the nth power of the q-derivative operator at x=0 for every function whose nth derivative at x=0 exists. We give a proof in both the real variable and the co…