International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 4, Pages 643-656
doi:10.1155/S0161171296000919
Generating new classes of orthogonal polynomials
Amílcar Branquinho1
and Francisco Marcellán2
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
Abstract
Given a sequence of monic orthogonal polynomials (MOPS), {Pn}, with respect to a quasi-definite linear functional u, we find necessary and sufficient conditions on the parameters an and bn for the sequence Pn(x)+anPn−1(x)+bnPn−2(x), n≥1P0(x)=1,P−1(x)=0 to be orthogonal. In particular, we can find explicitly the linear functional v 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 linear functional.