DLMF:16.4.E4 (Q5198): Difference between revisions

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imported>Admin
Property / Symbols used
 
Property / Symbols used: gamma function / rank
 
Normal rank
Property / Symbols used: gamma function / qualifier
 
test:

Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

\EulerGamma@{\NVar{z}}
Property / Symbols used: gamma function / qualifier
 
xml-id: C5.S2.E1.m2adec

Revision as of 14:30, 2 January 2020

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DLMF:16.4.E4
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    F 2 3 ( a , b , c a - b + 1 , a - c + 1 ; 1 ) = Γ ( 1 2 a + 1 ) Γ ( a - b + 1 ) Γ ( a - c + 1 ) Γ ( 1 2 a - b - c + 1 ) Γ ( a + 1 ) Γ ( 1 2 a - b + 1 ) Γ ( 1 2 a - c + 1 ) Γ ( a - b - c + 1 ) , Gauss-hypergeometric-pFq 3 2 𝑎 𝑏 𝑐 𝑎 𝑏 1 𝑎 𝑐 1 1 Euler-Gamma 1 2 𝑎 1 Euler-Gamma 𝑎 𝑏 1 Euler-Gamma 𝑎 𝑐 1 Euler-Gamma 1 2 𝑎 𝑏 𝑐 1 Euler-Gamma 𝑎 1 Euler-Gamma 1 2 𝑎 𝑏 1 Euler-Gamma 1 2 𝑎 𝑐 1 Euler-Gamma 𝑎 𝑏 𝑐 1 {\displaystyle{\displaystyle{{}_{3}F_{2}}\left({a,b,c\atop a-b+1,a-c+1};1% \right)=\frac{\Gamma\left(\frac{1}{2}a+1\right)\Gamma\left(a-b+1\right)\Gamma% \left(a-c+1\right)\Gamma\left(\frac{1}{2}a-b-c+1\right)}{\Gamma\left(a+1\right% )\Gamma\left(\frac{1}{2}a-b+1\right)\Gamma\left(\frac{1}{2}a-c+1\right)\Gamma% \left(a-b-c+1\right)},}}
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    Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    C5.S2.E1.m2adec
    0 references