New relations and identities for generalized hypergeometric coefficients
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.
scientific article; zbMATH DE number 56227
scientific article