On the zeros of some generalized hypergeometric functions
type: Item
instance of: scholarly article
title: On the zeros of some generalized hypergeometric functions
zbMATH Open document ID: 0951.33006
author: Haseo Ki
author: Young-One Kim
published in: Journal of Mathematical Analysis and Applications
publication date: 2000-05-07T00:00:00Z
review text: The paper is concerned with the confluent hypergeometric function \[ F= {_pF_p}(a_1,\dots, a_p; b_1,\dots, b_p; z). \] It is assumed that the parameters are real, no numerator parameter equals zero or a negative integer, and the denominator parameters are positive. Then, the author establishes the equivalence of the following assertions: (i) \(F\) has only a finite number of zeros; (ii) \(F\) has only real zeros; and (iii) there exist nonnegative integers \(m_1,\dots, m_p\) such that \(a_1= b_1+ m_1,\dots, a_p= b_p+ m_p\). Some examples are given to show that the assumptions cannot be relaxed. Besides the classical theory of hypergeometric functions the author also applies the Pólya-Schur theorem on multiplier sequences.
Mathematics Subject Classification ID: 33C20
zbMATH DE Number: 1439361
zbMATH Keywords: confluent hypergeometric function
zbMATH Keywords: multiplier sequences
reviewed by: Per W. Karlsson
MaRDI profile type: Publication
OpenAlex ID: W2057250552
cites work: Complex zero decreasing sequences
cites work: Periodic Sigma Functions
cites work: The Asymptotic Expansion of the Generalized Hypergeometric Function
DOI: 10.1006/JMAA.1999.6662
description: scientific article; zbMATH DE number 1439361