Gauss's \(_ 2F_ 1(1)\) cannot be generalized to \(_ 2F_ 1(x)\)
type: Item
instance of: scholarly article
title: Gauss's \(_ 2F_ 1(1)\) cannot be generalized to \(_ 2F_ 1(x)\)
zbMATH Open document ID: 0764.33001
DOI: 10.1016/0377-0427(92)90211-F
author: Doron Zeilberger
published in: Journal of Computational and Applied Mathematics
publication date: 1993-01-16T00:00:00Z
review text: Using ideas of J. Wimp and R. McIntosh, it is proved that Gauss's explicit evaluation of \(_ 2F_ 1(a,b;c;1)\) cannot be generalized to \(_ 2F_ 1(a,b;c;x)\), for arbitrary \(a\), \(b\), \(c\) and \(x\). A short proof of Wimp's theorem that asserts that \(_ 3F_ 2(a,b,c;d,e;1)\) cannot be expressed in closed form is also given.
Mathematics Subject Classification ID: 33C05
Mathematics Subject Classification ID: 33C20
zbMATH DE Number: 89597
zbMATH Keywords: explicit evaluation
zbMATH Keywords: Wimp's theorem
zbMATH Keywords: closed form
MaRDI profile type: Publication
cites work: Q4760447
cites work: Strange Evaluations of Hypergeometric Series
cites work: Q4057549
cites work: Generating Functions for Bessel and Related Polynomials
cites work: A proof that Euler missed. Apéry's proof of the irrationality of \(\zeta(3)\). An informal report
cites work: Irreducible recurrences and representation theorems for \(_ 3F_ 2(1)\)
full work available at URL: 0377-0427(92)90211-f
OpenAlex ID: W1984967714
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description: scientific article; zbMATH DE number 89597