Formula:10511

Digital Library of Mathematical Functions ID 35.7.E8

${\displaystyle{\displaystyle{{{}_{2}F_{1}}\left({a,b\atop c};\mathbf{T}\right)=\frac{\Gamma_{m}\left(c\right)\Gamma_{m}\left(c-a-b\right)}{\Gamma_{m}\left(c-a\right)\Gamma_{m}\left(c-b\right)}}\*{{}_{2}F_{1}}\left({a,b\atop a+b-c+\frac{1}{2}(m+1)};\mathbf{I}-\mathbf{T}\right),}}$

Constraint(s)

${\displaystyle{\displaystyle\Re(c),\Re(c-a-b)>\frac{1}{2}(m-1)}}$

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
• ${\displaystyle{\displaystyle\Gamma_{\NVar{m}}\left(\NVar{a}\right)}}$:
• ${\displaystyle{\displaystyle\Re}}$: real part
• ${\displaystyle{\displaystyle a}}$: complex variable
• ${\displaystyle{\displaystyle\mathbf{T}}}$: space of real symmetric matrices
• ${\displaystyle{\displaystyle b}}$: complex variable
• ${\displaystyle{\displaystyle c}}$: complex variable
• ${\displaystyle{\displaystyle m}}$: positive integer
 

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