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The distribution of zeros of a class of Jacobi polynomials
Author(s):
Marios
Charalambides;
George
Csordas
Journal:
Proc. Amer. Math. Soc.
138
(2010),
4345-4357.
MSC (2010):
Primary 33C47, 26C10;
Secondary 30C15, 33C52
Posted:
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  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:
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
Posted:
June 9, 2010
Communicated by:
Walter Van Assche
Copyright of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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