A new symmetry for Biedenharn's G-functions and classical hypergeometric series

DOI10.1016/0001-8708(85)90063-5zbMath0586.33013OpenAlexW2010612651MaRDI QIDQ1071918

Robert A. Gustafson, Stephen C. Milne

Publication date: 1985

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0001-8708(85)90063-5

zbMATH Keywords

tensor operatorswell-poised hypergeometric seriesbisymmetric polynomialsmultiple hypergeometric series well-poised in SU(n)

Mathematics Subject Classification ID

Connections of hypergeometric functions with groups and algebras, and related topics (33C80) Hypergeometric integrals and functions defined by them ((E), (G), (H) and (I) functions) (33C60) Classical hypergeometric functions, ({}_2F_1) (33C05)

Related Items

Basic hypergeometric series very well-poised in U(n), A new class of symmetric polynomials defined in terms of tableaux, New relations and identities for generalized hypergeometric coefficients, Identities in search of identity, Schur functions and the invariant polynomials characterizing U(n) tensor operators, An umbral calculus for polynomials characterizing U(n) tensor operators, The factorial Schur function, An algorithmic proof theory for hypergeometric (ordinary and ``\(q\)) multisum/integral identities, A q-analog of the \(_5F_4(1)\) summation theorem for hypergeometric series well-poised in \(SU(n)\), An elementary proof of the Macdonald identities for \(A_{\ell}^{(1)}\), A new symmetry related to SU(n) for clasical basic hypergeometric series, A q-analog of hypergeometric series well-poised in SU(n) and invariant G-functions, \(U(n)\) Wigner coefficients, the path sum formula, and invariant G-functions, A q-analog of transposition symmetry for invariant G-functions, A constant term identity featuring the ubiquitous (and mysterious) Andrews-Mills-Robbins-Rumsey numbers \(1, 2, 7, 42, 429, \dots\)

Cites Work

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• Schur functions and the invariant polynomials characterizing U(n) tensor operators
• An umbral calculus for polynomials characterizing U(n) tensor operators
• \(U(n)\) Wigner coefficients, the path sum formula, and invariant G-functions
• Hypergeometric series well-poised in SU(n) and a generalization of Biedenharn's G-functions
• The invariant polynomials characterizing \(U(n)\) tensor operators \(<p,q,\dots ,p,0,\dots ,0>\) having maximal null space
• On Hypergeometric Series Well-Poised in $SU(n)$