DLMF:8.10.E13 (Q2571)

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DLMF:8.10.E13
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    Statements

    Defining formula
    Γ ⁡ ( n , n ) Γ ⁡ ( n ) < 1 2 < Γ ⁡ ( n , n - 1 ) Γ ⁡ ( n ) , incomplete-Gamma 𝑛 𝑛 Euler-Gamma 𝑛 1 2 incomplete-Gamma 𝑛 𝑛 1 Euler-Gamma 𝑛 {\displaystyle{\displaystyle\frac{\Gamma\left(n,n\right)}{\Gamma\left(n\right)% }<\frac{1}{2}<\frac{\Gamma\left(n,n-1\right)}{\Gamma\left(n\right)},}}
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    DLMF id
    DLMF:8.10.E13
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    constraint
    n = 1 , 2 , 3 , … 𝑛 1 2 3 … {\displaystyle{\displaystyle n=1,2,3,\dots}}
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    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2abdec
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    incomplete gamma function
    Defining formula
    Γ ⁡ ( a , z ) incomplete-Gamma 𝑎 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C8.S2.E2.m2addec
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