Aufsatz in einer Fachzeitschrift
On fourth-order difference equations for orthogonal polynomials of a discrete variable: Derivation, factorization and solutions
Details zur Publikation
Autor(inn)en: | Foupouagnigni, M.; Koepf, W.; Ronveaux, A. |
Publikationsjahr: | 2003 |
Zeitschrift: | Journal of Difference Equations and Applications |
Seitenbereich: | 777-804 |
Jahrgang/Band : | 9 |
Heftnummer: | 9 |
Erste Seite: | 777 |
Letzte Seite: | 804 |
ISSN: | 1023-6198 |
eISSN: | 1563-5120 |
DOI-Link der Erstveröffentlichung: |
Zusammenfassung, Abstract
We derive and factorize the fourth-order difference equations satisfied by orthogonal polynomials obtained from some modifications of the recurrence coefficients of classical discrete orthogonal polynomials such as: the associated, the general co-recursive, co-recursive associated, co-dilated and the general co-modified classical orthogonal polynomials. Moreover, we find four linearly independent solutions of these fourth-order difference equations, and show how the results obtained for modified classical discrete orthogonal polynomials can be extended to modified semi-classical discrete orthogonal polynomials. Finally, we extend the validity of the results obtained for the associated classical discrete orthogonal polynomials with integer order of association from integers to reals.
We derive and factorize the fourth-order difference equations satisfied by orthogonal polynomials obtained from some modifications of the recurrence coefficients of classical discrete orthogonal polynomials such as: the associated, the general co-recursive, co-recursive associated, co-dilated and the general co-modified classical orthogonal polynomials. Moreover, we find four linearly independent solutions of these fourth-order difference equations, and show how the results obtained for modified classical discrete orthogonal polynomials can be extended to modified semi-classical discrete orthogonal polynomials. Finally, we extend the validity of the results obtained for the associated classical discrete orthogonal polynomials with integer order of association from integers to reals.
