Paper: The complementary polynomials and the Rodrigues operator of classical orthogonal polynomials

The complementary polynomials and the Rodrigues operator of classical orthogonal polynomials

Abstract

From the Rodrigues representation of polynomial eigenfunctions of a second order linear hypergeometric-type differential (difference or q-difference) operator, complementary polynomials (see, for example, [19]) for classical orthogonal polynomials are constructed using a straightforward method. Thus a generating function in a closed form is obtained. For the complementary polynomials we present a second order linear hypergeometric-type differential (difference or q-difference) operator, a three-term recursion and Rodrigues formulas which extend the results obtained in [19] for the standard derivative operator.

[19] Weber, H. J. Connections between real polynomial solutions of hypergeometric-type differential equations with Rodrigues formula. Cent. Eur. J. Math. 5 (2007), 415 — 427

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BibTeX

@article {MR2929017,
AUTHOR={Costas-Santos, R. S. and Marcellan, F.},
TITLE={The complementary polynomials and the {R}odrigues operator of classical orthogonal polynomials},
JOURNAL={Proc. Amer. Math. Soc.},
FJOURNAL={Proceedings of the American Mathematical Society},
VOLUME={140},
YEAR={2012},
NUMBER={10},
PAGES={3485--3493},
ISSN={0002-9939},
CODEN={PAMYAR},
MRCLASS={33C45 (33D45 34B24 39A13 42C05)},
MRNUMBER={2929017},
ZBL={1281.33006},
MRREVIEWER={Roelof Koekoek},
DOI={10.1090/S0002-9939-2012-11229-8},
URL={http://dx.doi.org/10.1090/S0002-9939-2012-11229-8},
}