DLMF:5.8.E1 (Q2085)

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DLMF:5.8.E1
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    Statements

    Defining formula
    Γ ⁡ ( z ) = lim k → ∞ ⁡ k ! ⁢ k z z ⁢ ( z + 1 ) ⁢ ⋯ ⁢ ( z + k ) , Euler-Gamma 𝑧 subscript → 𝑘 𝑘 superscript 𝑘 𝑧 𝑧 𝑧 1 ⋯ 𝑧 𝑘 {\displaystyle{\displaystyle\Gamma\left(z\right)=\lim_{k\to\infty}\frac{k!k^{z% }}{z(z+1)\cdots(z+k)},}}
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    DLMF id
    DLMF:5.8.E1
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    constraint
    z ≠ 0 , - 1 , - 2 , … 𝑧 0 1 2 … {\displaystyle{\displaystyle z\neq 0,-1,-2,\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.m2adec
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    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
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    Q11279
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C5.S1.XMD4.m1dec
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    Q11273
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C5.S1.XMD7.m1dec
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