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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The distribution of zeros of a class of Jacobi polynomials


Authors: Marios Charalambides and George Csordas
Journal: Proc. Amer. Math. Soc. 138 (2010), 4345-4357
MSC (2010): Primary 33C47, 26C10; Secondary 30C15, 33C52
Published electronically: June 9, 2010
MathSciNet review: 2680060
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Abstract: Polynomials whose coefficients are successive derivatives of a class of generalized Laguerre polynomials evaluated at $ x=0$ are shown to be stable. These polynomials can be expressed in terms of Jacobi polynomials. The authors also prove that a related family of polynomials, depending on a parameter, possess only real and negative zeros. A special class of stability-preserving operators is also investigated.


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Additional Information

Marios Charalambides
Affiliation: Mathematics, Physics, and Science Group, Frederick University, P.O. Box 24729, 1303 Nicosia, Cyprus
Email: bus.chm@fit.ac.cy

George Csordas
Affiliation: Department of Mathematics, University of Hawaii, Honolulu, Hawaii 96822
Email: george@math.hawaii.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10436-7
PII: S 0002-9939(2010)10436-7
Keywords: Jacobi polynomials, generalized Laguerre polynomials, multiplier sequences, $n$-sequences, positive pairs
Received by editor(s): June 10, 2009
Received by editor(s) in revised form: February 9, 2010
Published electronically: June 9, 2010
Communicated by: Walter Van Assche
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.