Formula:10489

Digital Library of Mathematical Functions ID 35.5.E4

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

Constraint(s)

${\displaystyle{\displaystyle\Re(\nu)>-1}}$
${\displaystyle{\displaystyle\mathbf{T}\in{\boldsymbol{\Omega}}}}$
${\displaystyle{\displaystyle\Re(\nu)>-1}}$

Symbols List

• ${\displaystyle{\displaystyle A_{\NVar{\nu}}\left(\NVar{\mathbf{T}}\right)}}$:
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\in}}$:
• ${\displaystyle{\displaystyle\mathrm{etr}\left(\NVar{\mathbf{X}}\right)}}$:
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\Re}}$: real part
• ${\displaystyle{\displaystyle\mathbf{S}}}$: identity matrix
• ${\displaystyle{\displaystyle\mathbf{T}}}$: space of real symmetric matrices
• ${\displaystyle{\displaystyle\mathbf{X}}}$: real symmetric matrix
• ${\displaystyle{\displaystyle{\boldsymbol{\Omega}}}}$: real symmetric matrix
• ${\displaystyle{\displaystyle m}}$: positive integer
• ${\displaystyle{\displaystyle\boldsymbol{\mathcal{S}}}}$: matrix of zeros
 

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