## The complementary polynomials and the Rodrigues operator of classical orthogonal polynomials

Costas-Santos, R. S. and Marcellan, F.**Proceedings of the American Mathematical Society**140, No. 10 (2012), 3485 — 3493

## 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}, }