The complementary polynomials and the Rodrigues operator of classical orthogonal polynomials

Costas-Santos, Roberto; Español, Francisco

doi:10.1090/S0002-9939-2012-11229-8

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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