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Generating new classes of orthogonal polynomials

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  • Amílcar Branquinho
  • Francisco Marcellán

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.

Suggested Citation

  • Amílcar Branquinho & Francisco Marcellán, 1996. "Generating new classes of orthogonal polynomials," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 19, pages 1-14, January.
  • Handle: RePEc:hin:jijmms:657910
    DOI: 10.1155/S0161171296000919
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    Cited by:

    1. Herbert Dueñas Ruiz & Francisco Marcellán & Alejandro Molano, 2019. "A Classification of Symmetric (1, 1)-Coherent Pairs of Linear Functionals," Mathematics, MDPI, vol. 7(2), pages 1-33, February.

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