The Complementary Polynomials and the Rodrigues Operator of Classical Orthogonal Polynomials
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چکیده
From the Rodrigues representation of polynomial eigenfunctions of a second order linear hypergeometric-type differential (difference or q-difference) 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 hypergeometric-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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تاریخ انتشار 2012