DLMF:35.8.E7 (Q9829): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
Property / constraint
 

( b 2 ) subscript 𝑏 2 {\displaystyle{\displaystyle\Re(b_{2})}}

\realpart@@{(b_{2})}
Property / constraint: ( b 2 ) subscript 𝑏 2 {\displaystyle{\displaystyle\Re(b_{2})}} / rank
 
Normal rank

Revision as of 18:31, 30 December 2019

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DLMF:35.8.E7
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    Statements

    F 2 3 ( a 1 , a 2 , a 3 b 1 , b 2 ; 𝐈 ) = Γ m ( b 1 ) Γ m ( b 2 ) Γ ( c ) Γ m ( a 1 ) Γ m ( c + a 2 ) Γ ( c + a 3 ) F 2 3 ( b 1 - a 1 , b 2 - a 2 , c c + a 2 , c + a 3 ; 𝐈 ) , Gauss-hypergeometric-of-matrix-pFq 3 2 subscript 𝑎 1 subscript 𝑎 2 subscript 𝑎 3 subscript 𝑏 1 subscript 𝑏 2 𝐈 multivariate-Euler-Gamma 𝑚 subscript 𝑏 1 multivariate-Euler-Gamma 𝑚 subscript 𝑏 2 Euler-Gamma 𝑐 multivariate-Euler-Gamma 𝑚 subscript 𝑎 1 multivariate-Euler-Gamma 𝑚 𝑐 subscript 𝑎 2 Euler-Gamma 𝑐 subscript 𝑎 3 Gauss-hypergeometric-of-matrix-pFq 3 2 subscript 𝑏 1 subscript 𝑎 1 subscript 𝑏 2 subscript 𝑎 2 𝑐 𝑐 subscript 𝑎 2 𝑐 subscript 𝑎 3 𝐈 {\displaystyle{\displaystyle{{}_{3}F_{2}}\left({a_{1},a_{2},a_{3}\atop b_{1},b% _{2}};\mathbf{I}\right)=\frac{\Gamma_{m}\left(b_{1}\right)\Gamma_{m}\left(b_{2% }\right)\Gamma\left(c\right)}{\Gamma_{m}\left(a_{1}\right)\Gamma_{m}\left(c+a_% {2}\right)\Gamma\left(c+a_{3}\right)}\*{{}_{3}F_{2}}\left({b_{1}-a_{1},b_{2}-a% _{2},c\atop c+a_{2},c+a_{3}};\mathbf{I}\right),}}
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    DLMF:35.8.E7
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    ( b 1 ) subscript 𝑏 1 {\displaystyle{\displaystyle\Re(b_{1})}}
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    ( b 2 ) subscript 𝑏 2 {\displaystyle{\displaystyle\Re(b_{2})}}
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