Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Asymptotic distributions of the zeros of a family of hypergeometric polynomials

Authors: Jian-Rong Zhou, H. M. Srivastava and Zhi-Gang Wang
Journal: Proc. Amer. Math. Soc. 140 (2012), 2333-2346
MSC (2010): Primary 33C05, 33C20; Secondary 30C15, 33C45
Posted: November 17, 2011
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Abstract | References | Similar Articles | Additional Information

Abstract: The main object of this paper is to consider the asymptotic distribution of the zeros of certain classes of the Gauss hypergeometric polynomials. Some classical analytic methods and techniques are used here to analyze the behavior of the zeros of the Gauss hypergeometric polynomials,

$\displaystyle \;_2F_1(-n, a; -n+b;z),$

where

is a nonnegative integer. Owing to the connection between the classical Jacobi polynomials and the Gauss hypergeometric polynomials, we prove a special case of a conjecture made by Martínez-Finkelshtein, Martínez-González and Orive. Numerical evidence and graphical illustrations of the clustering of the zeros on certain curves are generated by Mathematica (Version 4.0).

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