DLMF:16.4.E7 (Q5201)

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DLMF:16.4.E7
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    Statements

    Defining formula
    F 2 3 ⁡ ( a , 1 - a , c d , 2 ⁢ c - d + 1 ; 1 ) = π ⁢ Γ ⁡ ( d ) ⁢ Γ ⁡ ( 2 ⁢ c - d + 1 ) ⁢ 2 1 - 2 ⁢ c Γ ⁡ ( c + 1 2 ⁢ ( a - d + 1 ) ) ⁢ Γ ⁡ ( c + 1 - 1 2 ⁢ ( a + d ) ) ⁢ Γ ⁡ ( 1 2 ⁢ ( a + d ) ) ⁢ Γ ⁡ ( 1 2 ⁢ ( d - a + 1 ) ) , Gauss-hypergeometric-pFq 3 2 𝑎 1 𝑎 𝑐 𝑑 2 𝑐 𝑑 1 1 𝜋 Euler-Gamma 𝑑 Euler-Gamma 2 𝑐 𝑑 1 superscript 2 1 2 𝑐 Euler-Gamma 𝑐 1 2 𝑎 𝑑 1 Euler-Gamma 𝑐 1 1 2 𝑎 𝑑 Euler-Gamma 1 2 𝑎 𝑑 Euler-Gamma 1 2 𝑑 𝑎 1 {\displaystyle{\displaystyle{{}_{3}F_{2}}\left({a,1-a,c\atop d,2c-d+1};1\right% )=\frac{\pi\Gamma\left(d\right)\Gamma\left(2c-d+1\right)2^{1-2c}}{\Gamma\left(% c+\frac{1}{2}(a-d+1)\right)\Gamma\left(c+1-\frac{1}{2}(a+d)\right)\Gamma\left(% \frac{1}{2}(a+d)\right)\Gamma\left(\frac{1}{2}(d-a+1)\right)},}}
    0 references
    DLMF id
    DLMF:16.4.E7
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2acdec
    0 references
    Q11125
    Defining formula
    F q p ⁡ ( a 1 , … , a p ; b 1 , … , b q ; z ) Gauss-hypergeometric-pFq 𝑝 𝑞 subscript 𝑎 1 … subscript 𝑎 𝑝 subscript 𝑏 1 … subscript 𝑏 𝑞 𝑧 {\displaystyle{\displaystyle{{}_{\NVar{p}}F_{\NVar{q}}}\left(\NVar{a_{1},\dots% ,a_{p}};\NVar{b_{1},\dots,b_{q}};\NVar{z}\right)}}
    xml-id
    C16.S2.m1addec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
    0 references
    Q11693
    Defining formula
    a , a 1 , … , a p 𝑎 subscript 𝑎 1 … subscript 𝑎 𝑝 {\displaystyle{\displaystyle a,a_{1},\ldots,a_{p}}}
    xml-id
    C16.S1.XMD4.m1edec
    0 references
     
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