The complementary polynomials and the Rodrigues operator of classical orthogonal polynomials
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- by Roberto S. Costas-Santos and Francisco Marcellán Español PDF
- Proc. Amer. Math. Soc. 140 (2012), 3485-3493 Request permission
Abstract:
From the Rodrigues representation of polynomial eigenfunctions of a second order linear hypergeometric-type differential (difference or $q$-differ- ence) operator, complementary polynomials 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 hyper- geometric-type differential (difference or $q$-difference) operator, a three-term recursion and Rodrigues formulas which extend the results obtained by H. J. Weber for the standard derivative operator.
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Additional Information
- Roberto S. Costas-Santos
- Affiliation: Departamento de Matemáticas, Facultad de Ciencias, Universidad de Alcalá, 28871 Alcalá de Henares, Spain
- Email: rscosa@gmail.com, roberto.costas@uah.es
- Francisco Marcellán Español
- Affiliation: Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Spain
- Email: pacomarc@ing.uc3m.es
- Received by editor(s): February 11, 2011
- Received by editor(s) in revised form: April 8, 2011
- Published electronically: February 20, 2012
- Additional Notes: The first author acknowledges financial support from Dirección General de Investigación del Ministerio de Ciencia e Innovación of Spain under grant MTM2009-12740-C03-01 and from the program of postdoctoral grants (Programa de becas postdoctorales)
The second author acknowledges financial support from Dirección General de Investigación del Ministerio de Ciencia e Innovación of Spain under grant MTM 2009-12740-C03-01. - Communicated by: Walter Van Assche
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 140 (2012), 3485-3493
- MSC (2010): Primary 33C45; Secondary 34B24, 42C05
- DOI: https://doi.org/10.1090/S0002-9939-2012-11229-8
- MathSciNet review: 2929017