International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 4, Pages 643-656
Generating new classes of orthogonal polynomials
1Departamento de Matemática, FCTUC, Universidade de Coimbra, Apartado 3008, Coimbra 3000, Portugal
2Departamento de Ingeniería, Escuela Politécnica Superior, Universidad Carlos III, C. Butarque, 15, Leganés-Madrid 28911, Spain
Received 28 September 1994; Revised 15 December 1994
Copyright © 1996 Amílcar Branquinho and Francisco Marcellán. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Given a sequence of monic orthogonal polynomials (MOPS), , with respect
to a quasi-definite linear functional , we find necessary and sufficient conditions on the parameters
for the sequence
to be orthogonal. In particular, we can find explicitly the linear functional such that the new
sequence is the corresponding family of orthogonal polynomials. Some applications for Hermite
and Tchebychev orthogonal polynomials of second kind are obtained.
We also solve a problem of this type for orthogonal polynomials with respect to a Hermitian