# Hypergeometric Functions I

@article{MacDonald2013HypergeometricFI, title={Hypergeometric Functions I}, author={Ian G. MacDonald}, journal={arXiv: Classical Analysis and ODEs}, year={2013} }

This is the typewritten version of a handwritten manuscript which was completed by Ian G. Macdonald in 1987 or 1988. The manuscript is a very informal working paper, never intended for formal publication. Nevertheless, copies of the manuscript have circulated widely, giving rise to quite a few citations in the subsequent 25 years. Therefore it seems justified to make the manuscript available for the whole mathematical community. The author kindly gave his permission that a typewritten version… Expand

#### Paper Mentions

#### 10 Citations

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C 2013 Society for Industrial and Applied Mathematics Eigenvalue Distributions of Beta-wishart Matrices *

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We derive explicit expressions for the distributions of the extreme eigenvalues of the Beta-Wishart random matrices in terms of the hypergeometric function of a matrix argument. These results… Expand

Okounkov's BC-type interpolation Macdonald polynomials and their q=1 limit

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This paper surveys eight classes of polynomials associated with $A$-type and $BC$-type root systems: Jack, Jacobi, Macdonald and Koornwinder polynomials and interpolation (or shifted) Jack and… Expand

Eigenvalue distributions of beta-Wishart matrices

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- 2014

We derive explicit expressions for the distributions of the extreme eigenvalues of the beta-Wishart random matrices in terms of the hypergeometric function of a matrix argument. These results… Expand

Eigenvalue statistics for the sum of two complex Wishart matrices

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- 2014

The sum of independent Wishart matrices, taken from distributions with unequal covariance matrices, plays a crucial role in multivariate statistics, and has applications in the fields of quantitative… Expand

Universal Behavior of the Corners of Orbital Beta Processes

- Mathematics, Physics
- International Mathematics Research Notices
- 2019

There is a unique unitarily-invariant ensemble of $N\times N$ Hermitian matrices with a fixed set of real eigenvalues $a_1> \dots > a_N$. The joint eigenvalue distribution of the $(N-1)$ top-left… Expand

Beta Distributions and Sonine Integrals for Bessel Functions on Symmetric Cones

- Mathematics
- 2018

There exist several multivariate extensions of the classical Sonine integral representation for Bessel functions of some index $\mu+ \nu$ with respect to such functions of lower index $\mu.$ For… Expand

Positive intertwiners for Bessel functions of type B

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- 2019

Let $V_k$ denote Dunkl's intertwining operator for the root sytem $B_n$ with multiplicity $k=(k_1,k_2)$ with $k_1\geq 0, k_2>0$. It was recently shown that the positivity of the operator… Expand

PROPERTIES OF THE INVERSE OF A NONCENTRAL WISHART MATRIX

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- 2021

The inverse of a noncentral Wishart matrix occurs in a variety of contexts in multivariate statistical work, including instrumental variables (IV) regression, but there has been very little work on… Expand

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