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


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

AMER MATHEMATICAL SOC (AMS) | ISSN: 0002-9939 | JCR┬« 2012 Impact Factor: 0.609 - MATHEMATICS — position: 128/296 (Q2/T2)

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},
}