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|Author(s):||Howard S. Cohl; Connor M. MacKenzie;|
|Title:||Generalization and specializations of generating functions for Jacobi, Gegenbauer, Chebyshev and Legendre polynomials with definite integrals|
|Published:||January 15, 2014|
|Abstract:||In this paper we generalize and specialize generating functions for classical orthogonal polynomials, namely Jacobi, Gegenbauer, Chebyshev and Legendre polynomials. We derive a generalization of the generating function for Gegenbauer polynomials through extension a two element sequence of generating functions for Jacobi polynomials. Specializations of generating functions are accomplished through the re-expression of Gauss hypergeometric functions in terms of less general functions. Definite integrals which correspond to the presented orthogonal polynomial series expansions are also given.|
|Citation:||Journal of Classical Analysis|
|Pages:||pp. 17 - 33|
|Keywords:||Othogonal polynomials, Generating functions, Gauss hypergeometric function, Eigenfunction expansions, Definite integrals|
|DOI:||http://dx.doi.org/10.7153/jca-03-02 (Note: May link to a non-U.S. Government webpage)|
|PDF version:||Click here to retrieve PDF version of paper (174KB)|