New relations and identities for generalized hypergeometric coefficients
type: Item
instance of: scholarly article
title: New relations and identities for generalized hypergeometric coefficients
zbMATH Open document ID: 0746.33013
DOI: 10.1016/0196-8858(92)90004-G
author: L. C. Biedenharn
author: Adam M. Bincer
author: M. A. Lohe
author: J. D. Louck
published in: Advances in Applied Mathematics
publication date: 1992-09-26T00:00:00Z
review text: The subject of generalized hypergeometric coefficients has its origins in the problem of constructing tensor operators for compact Lie groups such as \(SU(3)\). This work, which (in the authors' words) completes a series of seven previous papers, proves several fundamental identities for these coefficients written \(\langle_ 2{\mathcal F}_ 1(a,b;c)|\lambda)\rangle\), where \(\lambda\) is a partition of some finite set. The coefficients generalize Gauss' hypergeometric function \(_ 2F_ 1\), while two identities generalize Bailey's and Saalschütz's formulas. Many results concern special polynomials, symmetric functions of several variables, and special functions of mathematical physics: they are presented for their own right. But most of these problems grew out of studying irreducible representations of \(SU(3)\) and their tensor products and was mainly motivated by physics.
Mathematics Subject Classification ID: 33C80
Mathematics Subject Classification ID: 33C20
Mathematics Subject Classification ID: 22E70
zbMATH DE Number: 56227
zbMATH Keywords: generalized hypergeometric coefficients
zbMATH Keywords: tensor operators
zbMATH Keywords: compact Lie groups
reviewed by: Gert Roepstorff
MaRDI profile type: Publication
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full work available at URL: 0196-8858(92)90004-g
OpenAlex ID: W2019433341
description: scientific article; zbMATH DE number 56227