## 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
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## 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’s 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’s 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