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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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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

Abstract:

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: harimsri@math.uvic.ca
  • Jian-Rong Zhou
  • Affiliation: Department of Mathematics, Foshan University, Foshan 528000, Guangdong, People鈥檚 Republic of China
  • Email: zhoujianrong2008@yahoo.com.cn
  • 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: wangmath@163.com
  • 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: https://doi.org/10.1090/S0025-5718-2011-02409-9
  • MathSciNet review: 2785478