Constant term identities and hypergeometric functions on spaces of Hermitian matrices
type: Item
instance of: scholarly article
title: Constant term identities and hypergeometric functions on spaces of Hermitian matrices
zbMATH Open document ID: 0767.33010
DOI: 10.1016/0378-3758(93)90040-D
author: Kenneth I. Gross
author: Donald Richards
published in: Journal of Statistical Planning and Inference
publication date: 1993-05-16T00:00:00Z
review text: The authors give some corollaries of a theorem on hypergeometric functions of a matrix variable which they will publish elsewhere. They note as special cases some identities that have unity on one side. An example is \[ 1=\sum_{k=1}^ n {_ p F_ q}(-n+1,a_ 2,\dots,a_ p; b_ 1,\dots,b_ q; s_ k)\prod_{{{i=1} \atop {i\neq k}}}^ n {s_ i \over {s_ i-s_ k}}, \] which involves only the classical hypergeometric series. Finally, some connections with basic hypergeometric series are mentioned.
Mathematics Subject Classification ID: 33C80
Mathematics Subject Classification ID: 33C20
Mathematics Subject Classification ID: 22E30
zbMATH DE Number: 168234
zbMATH Keywords: zonal polynomial
zbMATH Keywords: hypergeometric function of a matrix variable
zbMATH Keywords: Schur function
reviewed by: Per W. Karlsson
MaRDI profile type: Publication
cites work: Q4040884
cites work: Special Functions of Matrix Argument. I: Algebraic Induction, Zonal Polynomials, and Hypergeometric Functions
cites work: Total positivity, spherical series, and hypergeometric functions of matrix argument
cites work: Hypergeometric functions on complex matrix space
cites work: Distributions of Matrix Variates and Latent Roots Derived from Normal Samples
cites work: Q3477451
cites work: Q3977562
Wikidata QID: Q127333755
full work available at URL: 0378-3758(93)90040-d
OpenAlex ID: W2046945187
description: scientific article; zbMATH DE number 168234