DLMF:15.4.E28 (Q5012)

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DLMF:15.4.E28
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    F ( a , b ; 1 2 a + 1 2 b + 1 2 ; 1 2 ) = π Γ ( 1 2 a + 1 2 b + 1 2 ) Γ ( 1 2 a + 1 2 ) Γ ( 1 2 b + 1 2 ) . Gauss-hypergeometric-F 𝑎 𝑏 1 2 𝑎 1 2 𝑏 1 2 1 2 𝜋 Euler-Gamma 1 2 𝑎 1 2 𝑏 1 2 Euler-Gamma 1 2 𝑎 1 2 Euler-Gamma 1 2 𝑏 1 2 {\displaystyle{\displaystyle F\left(a,b;\tfrac{1}{2}a+\tfrac{1}{2}b+\tfrac{1}{% 2};\tfrac{1}{2}\right)=\sqrt{\pi}\frac{\Gamma\left(\tfrac{1}{2}a+\tfrac{1}{2}b% +\tfrac{1}{2}\right)}{\Gamma\left(\tfrac{1}{2}a+\tfrac{1}{2}\right)\Gamma\left% (\tfrac{1}{2}b+\tfrac{1}{2}\right)}.}}
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    DLMF:15.4.E28
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    Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    C5.S2.E1.m2afdec
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    F ( a , b ; c ; z ) Gauss-hypergeometric-F 𝑎 𝑏 𝑐 𝑧 {\displaystyle{\displaystyle F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}
    C15.S2.E1.m2azdec
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aadec
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    a 𝑎 {\displaystyle{\displaystyle a}}
    C15.S1.XMD4.m1udec
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    b 𝑏 {\displaystyle{\displaystyle b}}
    C15.S1.XMD5.m1idec
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