Formula:10487

Digital Library of Mathematical Functions ID 35.5.E2

${\displaystyle{\displaystyle A_{\nu}\left(\mathbf{T}\right)=A_{\nu}\left(\boldsymbol{{0}}\right)\sum_{k=0}^{\infty}\frac{(-1)^{k}}{k!}\sum_{|\kappa|=k}\frac{1}{{\left[\nu+\frac{1}{2}(m+1)\right]_{\kappa}}}Z_{\kappa}\left(\mathbf{T}\right),}}$

Constraint(s)

${\displaystyle{\displaystyle\nu\in\mathbb{C}}}$
${\displaystyle{\displaystyle\nu\in\mathbb{C}}}$
${\displaystyle{\displaystyle\mathbf{T}\in\boldsymbol{\mathcal{S}}}}$

Symbols List

• ${\displaystyle{\displaystyle A_{\NVar{\nu}}\left(\NVar{\mathbf{T}}\right)}}$:
• ${\displaystyle{\displaystyle\mathbb{C}}}$:
• ${\displaystyle{\displaystyle\in}}$:
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle{\left[\NVar{a}\right]_{\NVar{\kappa}}}}}$: partitional shifted factorial
• ${\displaystyle{\displaystyle Z_{\NVar{\kappa}}\left(\NVar{\mathbf{T}}\right)}}$:
• ${\displaystyle{\displaystyle\mathbf{T}}}$: space of real symmetric matrices
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle m}}$: positive integer
• ${\displaystyle{\displaystyle\boldsymbol{\mathcal{S}}}}$: matrix of zeros
 

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