On properties of hypergeometric functions of three variables, \(F_ M\) and \(F_ G\)
type: Item
instance of: scholarly article
title: On properties of hypergeometric functions of three variables, \(F_ M\) and \(F_ G\)
zbMATH Open document ID: 0682.33001
DOI: 10.1007/BF02844643
author: Megumi Saigo
publication date: 1988-01-01T00:00:00Z
review text: The triple hypergeometric series \(F_ M(x,y,z)\) and \(F_ G(x,y,z)\) are investigated near certain points on the boundary of the region of convergence, e.g. \(x+z=1\) with \(x>0\), under certain constraints upon the parameters. Four asymptotic expressions are derived, from which it is seen that the boundary points considered are logarithmic singularities. \(F_ G\) and \(F_ M\) are here expressed in terms of Srivastava's \(F^{(3)}\), Gauß' \({}_ 2F_ 1\), the logarithmic derivative of the Gamma functions, and elementary functions. The four expressions are too complicated to reproduce here. The derivations are based upon similar results for simpler hypergeometric functions.
Mathematics Subject Classification ID: 33C05
zbMATH DE Number: 4116942
zbMATH Keywords: Saran functions
zbMATH Keywords: triple hypergeometric functions
zbMATH Keywords: boundary of region of convergence
reviewed by: Per W. Karlsson
MaRDI profile type: Publication
cites work: Q5518575
cites work: Q3905658
cites work: Q3898756
cites work: Q3905659
cites work: Q3039695
cites work: Q3345085
cites work: Multiplication of fractional calculus operators and boundary value problems involving the Euler-Darboux equation
full work available at URL: https://doi.org/10.1007/bf02844643
OpenAlex ID: W1969177734
published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article; zbMATH DE number 4116942