Bounds for zeros of Meixner and Kravchuk polynomials

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Authors

Jooste, Alta
Jordaan, Kerstin Heidrun

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Publisher

Cambridge University Press

Abstract

The zeros of certain different sequences of orthogonal polynomials interlace in a well-defined way. The study of this phenomenon and the conditions under which it holds lead to a set of points that can be applied as bounds for the extreme zeros of the polynomials. We consider different sequences of the discrete orthogonal Meixner and Kravchuk polynomials and use mixed three-term recurrence relations, satisfied by the polynomials under consideration, to identify bounds for the extreme zeros of Meixner and Kravchuk polynomials.

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Keywords

Kravchuk polynomials, Meixner polynomials

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Citation

Jooste, A & Jordaan, KH 2014, 'Bounds for zeros of Meixner and Kravchuk polynomials', LMS Journal of Computation and Mathematics, vol. 17, no. 1, pp. 47-57.