Asymptotic distributions of the zeros of certain classes of hypergeometric functions and polynomials

H. M. Srivastava, Jian-Rong Zhou, Zhi-Gang Wang
2011 Mathematics of Computation  
The main object of this paper is to consider the asymptotic distribution of the zeros of certain classes of the Clausenian hypergeometric 3 F 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: where n is a nonnegative integer. Some families of the hypergeometric 3 F 2 functions, which are connected (by means of a hypergeometric reduction formula) with the Gauss
more » ... Gauss hypergeometric polynomials of the form 2 F 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).
doi:10.1090/s0025-5718-2011-02409-9 fatcat:lsgvtvz67rhdlhxi3ury3fwgyi