Formula:10500

Digital Library of Mathematical Functions ID 35.6.E7

${\displaystyle{\displaystyle{{}_{1}F_{1}}\left({a\atop b};\mathbf{T}\right)=\mathrm{etr}\left(\mathbf{T}\right){{}_{1}F_{1}}\left({b-a\atop b};-\mathbf{T}\right).}}$

Symbols List

• ${\displaystyle{\displaystyle{{}_{\NVar{p}}F_{\NVar{q}}}\left(\NVar{a_{1},\dots,a_{p}};\NVar{b_{1},\dots,b_{q}};\NVar{\mathbf{T}}\right)}}$: generalized hypergeometric function of matrix argument
• ${\displaystyle{\displaystyle\mathrm{etr}\left(\NVar{\mathbf{X}}\right)}}$:
• ${\displaystyle{\displaystyle a}}$: complex variable
• ${\displaystyle{\displaystyle\mathbf{T}}}$: space of real symmetric matrices
• ${\displaystyle{\displaystyle b}}$: complex variable
 

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