Zeros of Hypergeometric Functions

被引：0
作者：
Kathryn Boggs
Peter Duren
机构：
[1] University of Michigan,Department of Mathematics, Undergraduate Programs Office
[2] University of Michigan,Department of Mathematics
来源：
Computational Methods and Function Theory | 2001年 / 1卷 / 1期
关键词：
Hypergeometric functions; hypergeometric polynomials; Jacobi polynomials; zeros; Euler integral; asymptotic curves; 33C05; 30C15; 33C45;
D O I：
10.1007/BF03320990
中图分类号：
学科分类号：
摘要：
For certain ranges of parameters, it is shown that the hypergeometric function F(a, b; b+1; z) has no zeros in a specified half-plane. It is also shown that the zeros of the hypergeometric polynomials \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F(-n,\ kn\ + \ell\ + 1;\ kn\ + \ell\ + 2;\ z)$$\end{document} cluster on one loop of a specified lemniscate. Other results then follow from quadratic relations.
引用
收藏
页码：275 / 287
页数：12
相关论文
共 15 条
[1]  
Borwein P B(1995)Incomplete rational approximation in the complex plane Constr. Approx. 11 85-106
[2]  
Chen W(1999)Asymptotic zero distribution of hypergeometric polynomials Numerical Algorithms 21 147-156
[3]  
Driver K(2000)Zeros of hypergeometric polynomials F(−n, Indag. Math. 11 43-51
[4]  
Duren P(2001); 2b; Constr. Approx. 17 169-179
[5]  
Driver K(2001)) J. Comput. Appl. Math. 135 293-301
[6]  
Duren P(2001)Trajectories of the zeros of hypergeometric polynomials J. Approx. Theory 110 74-87
[7]  
Driver K(2001)(− J. Approx. Theory 111 329-343
[8]  
Duren P(2002), Proc. Amer. Math. Soc. 130 707-713
[9]  
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[10]  
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