Hahn, Jacobi, and Krawtchouk polynomials of several variables
Copyright policy )Hahn, Jacobi, and Krawtchouk polynomials of several variables
Hahn polynomials of several variables can be defined by using the Jacobi polynomials on the simplex as a generating function. Starting from this connection, a number of properties for these two families of orthogonal polynomials are derived. It is shown that the Hahn polynomials appear as connecting coefficients between several families of orthogonal polynomials on the simplex. Closed-form formulas are derived for the reproducing kernels of the Hahn polynomials and Krawtchouck polynomials. As an application, the Poisson kernels for the Hahn polynomials and the Krawtchouck polynomials are shown to be nonnegative.
22 pages
- University of Oregon United States
- University of Oregon Eugene United States
33C50, 33C70, Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable, reproducing kernel, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Jacobi polynomial, Poisson kernels, Krawtchouk polynomial, Hahn polynomial, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics
33C50, 33C70, Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable, reproducing kernel, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Jacobi polynomial, Poisson kernels, Krawtchouk polynomial, Hahn polynomial, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics
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