DLMF:15.4.E28 (Q5012)

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DLMF:15.4.E28
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    Statements

    test
    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)}.}}
    0 references
    DLMF id
    DLMF:15.4.E28
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2afdec
    0 references
     
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