Formula:10503

Digital Library of Mathematical Functions ID 35.6.E10

${\displaystyle{\displaystyle\lim_{a\to\infty}\Gamma_{m}\left(a\right)\Psi\left(a+\nu;\nu+\tfrac{1}{2}(m+1);a^{-1}\mathbf{T}\right)=B_{\nu}\left(\mathbf{T}\right).}}$

Symbols List

• ${\displaystyle{\displaystyle B_{\NVar{\nu}}\left(\NVar{\mathbf{T}}\right)}}$: Bessel function of matrix argument (second kind)
• ${\displaystyle{\displaystyle\Psi\left(\NVar{a};\NVar{b};\NVar{\mathbf{T}}\right)}}$: confluent hypergeometric function of matrix argument (second kind)
• ${\displaystyle{\displaystyle\Gamma_{\NVar{m}}\left(\NVar{a}\right)}}$:
• ${\displaystyle{\displaystyle a}}$: complex variable
• ${\displaystyle{\displaystyle\mathbf{T}}}$: space of real symmetric matrices
• ${\displaystyle{\displaystyle m}}$: positive integer
 

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