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Jooste, A.* ; Jordaan, K.* ; Toókos, F.

On the zeros of Meixner polynomials.

Numer. Math. 124, 57-71 (2013)
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We investigate the zeros of a family of hypergeometric polynomials Mn(x; β, c) = (β)n 2F1(−n,−x; β; 1 − 1c ), n ∈ N, known as Meixner polynomials, that are orthogonal on (0,∞) with respect to a discrete measure for β > 0 and 0 < c < 1. When β = −N, N ∈ N and c = p p−1 , the polynomials Kn(x; p, N) = (−N)n 2F1(−n,−x;−N; 1 p ), n = 0, 1, . . . , N, 0 < p < 1 are referred to as Krawtchouk polynomials. We prove results for the zero location of the orthogonal polynomials Mn(x; β, c), c < 0 and n < 1 − β, the quasi-orthogonal polynomials Mn(x; β, c), −k < β < −k + 1, k = 1, . . . , n − 1 and 0 < c < 1 or c > 1, as well as the polynomials Kn(x; p, N) with non-Hermitian orthogonality for 0 < p < 1 and n = N+1, N+2, . . ..We also showthat the polynomials Mn(x; β, c), β ∈ R are real-rooted when c → 0.
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Publikationstyp Artikel: Journalartikel
Dokumenttyp Wissenschaftlicher Artikel
Schlagwörter Mathematics Subject Classification (2000): 33C45, 42C05; Classical Orthogonal Polynomials ; Krawtchouk Polynomials ; Nonstandard Parameters ; Strong Asymptotics ; Discrete ; Sequences
ISSN (print) / ISBN 0029-599x
e-ISSN 0945-3245
Zeitschrift Numerische Mathematik
Quellenangaben Band: 124, Heft: 1, Seiten: 57-71 Artikelnummer: , Supplement: ,
Verlag Springer
Verlagsort Berlin ; Heidelberg [u.a.]
Begutachtungsstatus Peer reviewed