Generalizations and specializations of generating functions for Jacobi, Gegenbauer, Chebyshev and Legendre polynomials with definite integrals
Copyright policy )Generalizations and specializations of generating functions for Jacobi, Gegenbauer, Chebyshev and Legendre polynomials with definite integrals
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.
- Information Technology Laboratory United States
- National Institute of Standards and Technology United States
- Westminster College of Salt Lake City United States
33C45, 05A15, 33C05, 34L10, 30E20, Exact enumeration problems, generating functions, definite integrals, Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Classical hypergeometric functions, \({}_2F_1\), Mathematics - Classical Analysis and ODEs, Gauss hypergeometric function, generating functions, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane, othogonal polynomials, eigenfunction expansions
33C45, 05A15, 33C05, 34L10, 30E20, Exact enumeration problems, generating functions, definite integrals, Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Classical hypergeometric functions, \({}_2F_1\), Mathematics - Classical Analysis and ODEs, Gauss hypergeometric function, generating functions, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane, othogonal polynomials, eigenfunction expansions
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