Generating new classes of orthogonal polynomials

Amílcar Branquinho and Francisco Marcellán

International Journal of Mathematics and Mathematical Sciences, 1996, vol. 19, 1-14

Abstract:

Given a sequence of monic orthogonal polynomials (MOPS), { P n } , with respect to a quasi-definite linear functional u , we find necessary and sufficient conditions on the parameters a n and b n for the sequence P n ( x ) + a n P n − 1 ( x ) + b n P n − 2 ( x ) ,       n ≥ 1 P 0 ( 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.

Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:657910

DOI: 10.1155/S0161171296000919

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