Multiple Wilson and Jacobi–Piñeiro polynomials
Copyright policy )Multiple Wilson and Jacobi–Piñeiro polynomials
We introduce multiple Wilson polynomials, which give a new example of multiple orthogonal polynomials (Hermite-Pade polynomials) of type II. These polynomials can be written as a Jacobi-Pineiro transform, which is a generalization of the Jacobi transform for Wilson polynomials, found by T.H. Koornwinder. Here we need to introduce Jacobi and Jacobi-Pineiro polynomials with complex parameters. Some explicit formulas are provided for both Jacobi-Pineiro and multiple Wilson polynomials, one of them in terms of Kampe de Feriet series. Finally we look at some limiting relations and construct a part of a multiple AT-Askey table.
22 pages, 2 figures
Mathematics(all), Numerical Analysis, Applied Mathematics, Multiple orthogonal polynomials, Other special orthogonal polynomials and functions, Hypergeometric functions, multiple orthogonal polynomials, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.), Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, Analysis, 33C45, 42C05, hypergeometric functions
Mathematics(all), Numerical Analysis, Applied Mathematics, Multiple orthogonal polynomials, Other special orthogonal polynomials and functions, Hypergeometric functions, multiple orthogonal polynomials, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.), Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, Analysis, 33C45, 42C05, hypergeometric functions
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