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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Asymptotic distributions of the zeros of certain classes of hypergeometric functions and polynomials
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by H. M. Srivastava, Jian-Rong Zhou and Zhi-Gang Wang PDF
Math. Comp. 80 (2011), 1769-1784 Request permission


The main object of this paper is to consider the asymptotic distribution of the zeros of certain classes of the Clausenian hypergeometric $\;_3F_2$ functions and polynomials. Some classical analytic methods and techniques are used here to analyze the behavior of the zeros of the Clausenian hypergeometric polynomials: \[ \;_3F_2(-n, \tau n+a, b;\tau n+c, -n+d;z),\] where $n$ is a nonnegative integer. Some families of the hypergeometric $_3F_2$ functions, which are connected (by means of a hypergeometric reduction formula) with the Gauss hypergeometric polynomials of the form \[ \;_2F_1(-n,kn+l+1;kn+l+2;z),\] are also investigated. Numerical evidence and graphical illustrations of the clustering of zeros on certain curves are generated by Mathematica (Version 4.0).
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Additional Information
  • H. M. Srivastava
  • Affiliation: Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada
  • Email:
  • Jian-Rong Zhou
  • Affiliation: Department of Mathematics, Foshan University, Foshan 528000, Guangdong, People鈥檚 Republic of China
  • Email:
  • Zhi-Gang Wang
  • Affiliation: School of Mathematics and Computing Science, Changsha University of Science and Technology, Yuntang Campus, Changsha 410114, Hunan, People鈥檚 Republic of China
  • Email:
  • Received by editor(s): December 1, 2009
  • Received by editor(s) in revised form: January 7, 2010
  • Published electronically: February 11, 2011
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 80 (2011), 1769-1784
  • MSC (2010): Primary 33C05, 33C20; Secondary 30C15, 33C45
  • DOI:
  • MathSciNet review: 2785478