Zeros of hypergeometric functions
type: Item
instance of: scholarly article
title: Zeros of hypergeometric functions
zbMATH Open document ID: 1009.33004
DOI: 10.1007/BF03320990
author: Kathryn Boggs
author: Peter Duren
published in: Computational Methods and Function Theory
publication date: 2003-05-01T00:00:00Z
review text: Here it is shown that the hypergeometric function \(F(a,b;b+1;z)\) has no zeros in a specified half-plane for certain ranges of parameters. It is also shown that the zeros of the hypergeometric polynomials \(F(-n,kn+ \ell+1; kn+ \ell+2;z)\) cluster on one loop of a specified lemniscate. Other results then follow from quadratic relations.
reviewed by: Som Prakash Goyal
Mathematics Subject Classification ID: 33C05
Mathematics Subject Classification ID: 30C15
Mathematics Subject Classification ID: 33C45
zbMATH DE Number: 1833069
zbMATH Keywords: hypergeometric functions
zbMATH Keywords: hypergeometric polynomials
zbMATH Keywords: Jacobi polynomials
zbMATH Keywords: series
zbMATH Keywords: Euler integral
MaRDI profile type: Publication
cites work: Q4222737
cites work: Incomplete rational approximation in the complex plane
cites work: Asymptotic zero distribution of hypergeometric polynomials
cites work: Zeros of the hypergeometric polynomials \(F(-n,b;2b;z)\)
cites work: Trajectories of the zeros of hypergeometric polynomials \(F(-n, b; 2b; z)\) for \(b< -\frac{1}{2}\)
cites work: Zeros of ultraspherical polynomials and the Hilbert-Klein formulas
cites work: Zeros of hypergeometric polynomials \(F(-n,b;-2n;z)\)
cites work: Asymptotic properties of zeros of hypergeometric polynomials
cites work: Canonical divisors in weighted Bergman spaces
cites work: Zeros of extremal functions in weighted Bergman spaces.
full work available at URL: https://doi.org/10.1007/bf03320990
OpenAlex ID: W2051735503
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description: scientific article; zbMATH DE number 1833069