Formula:10484

Digital Library of Mathematical Functions ID 35.4.E8

${\displaystyle{\displaystyle\int_{\boldsymbol{\Omega}}\mathrm{etr}\left(-\mathbf{T}\mathbf{X}\right)\,|\mathbf{X}|^{a-\frac{1}{2}(m+1)}Z_{\kappa}\left(\mathbf{X}\right)\mathrm{d}\mathbf{X}=\Gamma_{m}\left(a+\kappa\right)\,|\mathbf{T}|^{-a}Z_{\kappa}\left(\mathbf{T}^{-1}\right),}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\mathrm{etr}\left(\NVar{\mathbf{X}}\right)}}$:
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\Gamma_{\NVar{m}}\left(\NVar{a}\right)}}$:
• ${\displaystyle{\displaystyle Z_{\NVar{\kappa}}\left(\NVar{\mathbf{T}}\right)}}$:
• ${\displaystyle{\displaystyle a}}$: complex variable
• ${\displaystyle{\displaystyle\mathbf{T}}}$: space of real symmetric matrices
• ${\displaystyle{\displaystyle\mathbf{X}}}$: real symmetric matrix
• ${\displaystyle{\displaystyle{\boldsymbol{\Omega}}}}$: real symmetric matrix
• ${\displaystyle{\displaystyle m}}$: positive integer
 

Resources that cite this formula

No records found.