An identity involving partitional generalized binomial coefficients

Christopher Bingham

Journal of Multivariate Analysis, 1974, vol. 4, issue 2, 210-223

Abstract: Define coefficients (?[lambda]) by C[lambda](Ip + Z)/C[lambda](Ip) = [Sigma]k=0l [Sigma][varkappa][set membership, variant]k ([varkappa][lambda]) C?(Z)/C?(Ip), where the C[lambda]'s are zonal polynomials in p by p matrices. It is shown that C[varkappa](Z) etr(Z)/k! = [Sigma]l=k[infinity] [Sigma][lambda][set membership, variant]l ([varkappa][lambda]) C[lambda](Z)/l!. This identity is extended to analogous identities involving generalized Laguerre, Hermite, and other polynomials. Explicit expressions are given for all ([varkappa][lambda]), [varkappa] [set membership, variant] k, k

Keywords: Zonal; polynomials; generalized; binomial; coefficients; generalized; Laguerre; polynomials; generalized; Hermitian; polynomials; hypergeometric; functions; of; matrix; argument (search for similar items in EconPapers)
Date: 1974
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Citations: View citations in EconPapers (1)

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