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Jordaan, K.* ; Toókos, F.

Interlacing theorems for the zeros of some orthogonal polynomials from different sequences.

Appl. Numer. Math. 59, 2015-2022 (2009)
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We Study the interlacing properties of the zeros of orthogonal polynomials p(n) and r(m), m = n or n - 1 where {p(n)}(n=1)(infinity) and {r(m)}(m=1)(infinity) are different sequences of orthogonal polynomials. The results obtained extend a conjecture by Askey, that the zeros of Jacobi polynomials p(n) = P-n((alpha,beta)) and r(n) = P-n((gamma,beta)) n interlace when alpha < gamma <= alpha + 2, showing that the conjecture is true not only for Jacobi polynomials but also holds for Meixner, Meixner-Pollaczek, Krawtchouk and Hahn polynornials with continuously shifted parameters. Numerical examples are given to illustrate cases where the zeros do not separate each other.
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Publikationstyp Artikel: Journalartikel
Dokumenttyp Wissenschaftlicher Artikel
Schlagwörter Orthogonal polynomialS.; ZeroS.; Interlacing of zeroS.; Separation of zeroS.; Meixner polynomialS.; Krawtchouk polynomialS.; Meixner-Pollaczek polynomialS.; Hahn polynomials
ISSN (print) / ISBN 0168-9274
e-ISSN 1873-5460
Quellenangaben Band: 59, Heft: 8, Seiten: 2015-2022 Artikelnummer: , Supplement: ,
Verlag Elsevier
Begutachtungsstatus Peer reviewed