DLMF:16.4.E8 (Q5202)

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DLMF:16.4.E8
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    Statements

    Defining formula
    F 2 3 ⁡ ( - n , a , 1 - a d , 1 - d - 2 ⁢ n ; 1 ) = ( 1 2 ⁢ ( a + d ) ) n ⁢ ( 1 2 ⁢ ( d - a + 1 ) ) n ( 1 2 ⁢ d ) n ⁢ ( 1 2 ⁢ ( d + 1 ) ) n , Gauss-hypergeometric-pFq 3 2 𝑛 𝑎 1 𝑎 𝑑 1 𝑑 2 𝑛 1 Pochhammer 1 2 𝑎 𝑑 𝑛 Pochhammer 1 2 𝑑 𝑎 1 𝑛 Pochhammer 1 2 𝑑 𝑛 Pochhammer 1 2 𝑑 1 𝑛 {\displaystyle{\displaystyle{{}_{3}F_{2}}\left({-n,a,1-a\atop d,1-d-2n};1% \right)=\frac{{\left(\frac{1}{2}(a+d)\right)_{n}}{\left(\frac{1}{2}(d-a+1)% \right)_{n}}}{{\left(\frac{1}{2}d\right)_{n}}{\left(\frac{1}{2}(d+1)\right)_{n% }}},}}
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    DLMF id
    DLMF:16.4.E8
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    constraint
    n = 0 , 1 , … 𝑛 0 1 … {\displaystyle{\displaystyle n=0,1,\dots}}
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