On the order of starlikeness of hypergeometric functions
type: Item
instance of: scholarly article
title: On the order of starlikeness of hypergeometric functions
zbMATH Open document ID: 0598.30021
DOI: 10.1016/0022-247X(86)90329-X
published in: Journal of Mathematical Analysis and Applications
publication date: 1986-01-01T00:00:00Z
review text: An analytic function f in a domain D is called starlike of order \(\gamma <1\) if and only if \[ f(0)=0,\quad f'(0)=1\quad and\quad Re[zf'(z)/f(z)]>\gamma,\quad z\in D. \] \(S^*_{\gamma}\) denotes the set of these functions. The authors estimate the order of starlikeness of the hypergeometric functions \(u(z)=z_ 2F_ 1(a,b;c: \rho z)\). Some interesting applications and a confluent case have also been given.
Mathematics Subject Classification ID: 30C45
Mathematics Subject Classification ID: 33C05
zbMATH DE Number: 3964312
zbMATH Keywords: order of starlikeness
zbMATH Keywords: hypergeometric functions
zbMATH Keywords: confluent
author: Stephan Ruscheweyh
author: Vikramaditya Singh
MaRDI profile type: Publication
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cites work: Starlike Hypergeometric Functions
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full work available at URL: 0022-247x(86)90329-x
OpenAlex ID: W2094695796
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description: scientific article; zbMATH DE number 3964312