On zeros of discrete orthogonal polynomials
Copyright policy )On zeros of discrete orthogonal polynomials
The authors establish sharp inequalities for the extreme zeros of the classical discrete orthogonal polynomials: Charlier, Krawtchouk, Meixner, and Hahn. Their approach is based on the corresponding difference equations. For Charlier, Krawtchouk, and Meixner polynomials the function bounding the zero spacing is unimodal, meanwhile for the Hahn case different situations appear, depending on the parameters. Finally, they also provide lower bounds on the minimal distance between consecutive zeros.
- Brunel University United Kingdom
- Brunel University London United Kingdom
Meixner polynomials, Mathematics(all), Numerical Analysis, Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), Charlier polynomials, Applied Mathematics, 510, Zeros, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Hahn polynomials, Discrete orthogonal polynomials, zeros, Krawtchouk polynomials, Difference operators, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, Analysis
Meixner polynomials, Mathematics(all), Numerical Analysis, Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), Charlier polynomials, Applied Mathematics, 510, Zeros, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Hahn polynomials, Discrete orthogonal polynomials, zeros, Krawtchouk polynomials, Difference operators, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, Analysis
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