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International Journal of Mathematics and Mathematical Sciences - Volume 19 1996, Issue 4, Pages 643-656

Departamento de Matemática, FCTUC, Universidade de Coimbra, Apartado 3008, Coimbra 3000, Portugal

Departamento 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 Hindawi Publishing Corporation. 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, {Pn}, with respectto a quasi-definite linear functional u, we find necessary and sufficient conditions on the parametersan and bn for the sequencePnx+anPn−1x+bnPn−2x,   n≥1P0x=1,P−1x=0to be orthogonal. In particular, we can find explicitly the linear functional v such that the newsequence is the corresponding family of orthogonal polynomials. Some applications for Hermiteand Tchebychev orthogonal polynomials of second kind are obtained.

We also solve a problem of this type for orthogonal polynomials with respect to a Hermitianlinear functional.

Author: Amílcar Branquinho and Francisco Marcellán



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