Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4630694 | Applied Mathematics and Computation | 2011 | 7 Pages |
Abstract
We study the asymptotic distribution of the zeros of certain classes of Gauss hypergeometric polynomials. Classical analytic methods such as Watson's lemma and the method of steepest descents are used to analyze the large-n behavior of the zeros of the Gauss hypergeometric polynomials:2F1(-n,a;kn+b;z),2F1(-n,kn+c;kn+c+Ï;z)and2F1(-n,λ;-pn+ν;z),where n is a nonnegative integer, the constants k, a, Ï, λ > 0, p > 1, and b,c,νâR. Owing to the connection between Jacobi polynomials and Gauss hypergeometric polynomials, we prove a special case of a conjecture made by MartÃnez-Finkelshtein, MartÃnez-González, and Orive. Numerical evidence and graphical illustrations of the clustering of zeros on certain curves are generated by Mathematica (Version 4.0).
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Jian-Rong Zhou, Yu-Qiu Zhao,