New relations and identities for generalized hypergeometric coefficients

L. C. Biedenharn, A. M. Bincer, Max A. Lohe, J. D. Louck

    Research output: Contribution to journalComment/debate


    Generalized hypergeometric coefficients 〈pFq(a; b)|λ〉 enter into the problem of constructing matrix elements of tensor operators in the unitary groups and are the expansion coefficients of a multivariable symmetric function generalization pFq(a; b; z), z = (z1, z2,..., zt), of the Gauss hypergeometric function in terms of the Schur functions eλ(z), where λ = (λ1, λ2,..., λt) is an arbitrary partition. As befits their group-theoretic origin, identities for these generalized hypergeometric coefficients characteristically involve series summed over the Littlewood-Richardson numbers g(μνλ). Identities that may be interpreted as generalizations of the Bailey, Saalschütz,... identities are developed in this paper. Of particular interest is an identity which develops in a natural way a group-theoretically defined expansion over new inhomogeneous symmetric functions. While the relations obtained here are essential for the development of the properties of tensor operators, they are also of interest from the viewpoint of special functions.
    Original languageEnglish
    Pages (from-to)62-121
    Number of pages60
    JournalAdvances in Applied Mathematics
    Issue number1
    Publication statusPublished - 1992


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