# 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…

## 10 Citations

Riesz distributions and Laplace transform in the Dunkl setting of type A

- Mathematics
- 2019

We study Riesz distributions in the framework of rational Dunkl theory associated with root systems of type A. As an important tool, we employ a Laplace transform involving the associated Dunkl…

Branching Rules for Symmetric Hypergeometric Polynomials

- Mathematics, Physics
- 2016

Starting from a recently found branching formula for the six-parameter family of symmetric Macdonald-Koornwinder polynomials, we arrive by degeneration at corresponding branching rules for symmetric…

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

- 2013

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…

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

- Mathematics
- 2014

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…

Eigenvalue distributions of beta-Wishart matrices

- Mathematics
- 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…

Eigenvalue statistics for the sum of two complex Wishart matrices

- Physics, Mathematics
- 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…

Universal Behavior of the Corners of Orbital Beta Processes

- Mathematics, PhysicsInternational 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…

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…

Positive intertwiners for Bessel functions of type B

- Mathematics
- 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…

PROPERTIES OF THE INVERSE OF A NONCENTRAL WISHART MATRIX

- Mathematics
- 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…

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