An identity involving partitional generalized binomial coefficients

DOI10.1016/0047-259X(74)90014-1zbMath0284.05007OpenAlexW2010948864MaRDI QIDQ1844670

Christopher Bingham

Publication date: 1974

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0047-259x(74)90014-1

Mathematics Subject Classification ID

Multivariate distribution of statistics (62H10) Hypothesis testing in multivariate analysis (62H15) Exact enumeration problems, generating functions (05A15) Factorials, binomial coefficients, combinatorial functions (05A10) Combinatorial identities, bijective combinatorics (05A19) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Classical hypergeometric functions, ({}_2F_1) (33C05)

Related Items (18)

Asymptotic expansions of some matrix argument hypergeometric functions, with applications to macromolecules ⋮ PROPERTIES OF THE INVERSE OF A NONCENTRAL WISHART MATRIX ⋮ Invariant polynomials with two matrix arguments extending the zonal polynomials: Applications to multivariate distribution theory ⋮ Differential operators associated with zonal polynomials. I ⋮ Differential operators associated with zonal polynomials. II ⋮ On some formulas for weighted sum of invariant polynomials of two matrix arguments ⋮ The binomial formula for nonsymmetric Macdonald polynomials ⋮ On Bessel integrals for reducible degenerate principal series representations ⋮ Invariant Polynomials and Related Tests ⋮ Distributions of characteristic roots in multivariate analysis Part II. Non-Null Distribution ⋮ On a Fourier integral over SO(3) ⋮ A parametrization for independent variables of a two-matrix hypergeometric function ⋮ Distribution theory for some tests of independence of seemingly unrelated regressions ⋮ On the calculation of generalized binomial coefficients ⋮ Spherical functions on the Grassmann manifold and generalized Jacobi polynomials. I ⋮ Some combinatorial conjectures for shifted Jack polynomials ⋮ Complex generalized binomial coefficients ⋮ On the expansion of \(C^*_{\rho}(V+I)\) as a sum of zonal polynomials

Cites Work

• Unnamed Item
• Bessel functions of matrix argument
• On the distribution of the latent roots of a positive definite random symmetric matrix. I
• On the moments of elementary symmetric functions of the roots of two matrices
• The Distribution of Hotelling's Generalised $T_0^2$
• Asymptotic Expansions of the Non-Null Distributions of the Likelihood Ratio Criteria for Multivariate Linear Hypothesis and Independence
• Systems of Partial Differential Equations for Hypergeometric Functions of Matrix Argument
• Distributions of Matrix Variates and Latent Roots Derived from Normal Samples
• Some Non-Central Distribution Problems in Multivariate Analysis

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