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An identity involving partitional generalized binomial coefficients

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  • Bingham, Christopher

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

Suggested Citation

  • Bingham, Christopher, 1974. "An identity involving partitional generalized binomial coefficients," Journal of Multivariate Analysis, Elsevier, vol. 4(2), pages 210-223, June.
    • Handle: RePEc:eee:jmvana:v:4:y:1974:i:2:p:210-223
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    Cited by:

    1. Gaoyuan Wei & B. Eichinger, 1993. "Asymptotic expansions of some matrix argument hypergeometric functions, with applications to macromolecules," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(3), pages 467-475, September.

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