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

 

A new property of a class of Jacobi polynomials


Authors: George Csordas, Marios Charalambides and Fabian Waleffe
Journal: Proc. Amer. Math. Soc. 133 (2005), 3551-3560
MSC (2000): Primary 33C47, 26C10; Secondary 30C15, 33C52
Published electronically: June 6, 2005
MathSciNet review: 2163590
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Abstract: Polynomials whose coefficients are successive derivatives of a class of Jacobi polynomials evaluated at $x=1$ are stable. This yields a novel and short proof of the known result that the Bessel polynomials are stable polynomials. Stability-preserving linear operators are discussed. The paper concludes with three open problems involving the distribution of zeros of polynomials.


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Additional Information

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

Marios Charalambides
Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
Email: charalam@math.wisc.edu

Fabian Waleffe
Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
Email: waleffe@math.wisc.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07898-6
PII: S 0002-9939(05)07898-6
Keywords: Jacobi and Bessel polynomials, stability, real zeros of polynomials
Received by editor(s): May 28, 2004
Received by editor(s) in revised form: July 9, 2004
Published electronically: June 6, 2005
Communicated by: Carmen Chicone
Article copyright: © Copyright 2005 American Mathematical Society