IncBeta

Evaluates the incomplete Beta function of a matrix argument.

Evaluates the hypergeometric functions of a matrix argument,
which appear in random matrix theory. This is an implementation of
Koev & Edelman's algorithm (2006) <doi:10.1090/S0025-5718-06-01824-2>.

Stc3<a9>phane Laurent

HypergeoMat

Hypergeometric Function of a Matrix Argument

IncBeta function

<dl><dt>m</dt>
<dd>truncation weight of the summation, a positive integer</dd>
<dt>a, b</dt>
<dd>real or complex parameters with <code>Re(a)&gt;(p-1)/2</code> and
<code>Re(b)&gt;(p-1)/2</code>, where <code>p</code> is the dimension (the order of the
matrix)</dd>
<dt>x</dt>
<dd>either a real positive symmetric matrix or a complex positive
Hermitian matrix "smaller" than the identity matrix (i.e. <code>I-x</code> is
positive), or a numeric or complex vector, the eigenvalues of the matrix</dd></dl>

Arguments

Incomplete Beta function of a matrix argument — IncBeta

<dl>

<dt>m</dt>
<dd>truncation weight of the summation, a positive integer</dd>


<dt>a, b</dt>
<dd>real or complex parameters with <code>Re(a)&gt;(p-1)/2</code> and
<code>Re(b)&gt;(p-1)/2</code>, where <code>p</code> is the dimension (the order of the
matrix)</dd>


<dt>x</dt>
<dd>either a real positive symmetric matrix or a complex positive
Hermitian matrix "smaller" than the identity matrix (i.e. <code>I-x</code> is
positive), or a numeric or complex vector, the eigenvalues of the matrix</dd>

</dl>

IncBeta: Incomplete Beta function of a matrix argument

Description

Usage

Value

Arguments

References

Examples