DLMF:5.8.E2 (Q2086)

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DLMF:5.8.E2
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    Statements

    Defining formula
    1 Γ ⁡ ( z ) = z ⁢ e γ ⁢ z ⁢ ∏ k = 1 ∞ ( 1 + z k ) ⁢ e - z / k , 1 Euler-Gamma 𝑧 𝑧 superscript 𝑒 𝑧 superscript subscript product 𝑘 1 1 𝑧 𝑘 superscript 𝑒 𝑧 𝑘 {\displaystyle{\displaystyle\frac{1}{\Gamma\left(z\right)}=ze^{\gamma z}\prod_% {k=1}^{\infty}\left(1+\frac{z}{k}\right)e^{-z/k},}}
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    DLMF id
    DLMF:5.8.E2
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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.m2aadec
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    Euler’s constant
    Defining formula
    γ {\displaystyle{\displaystyle\gamma}}
    xml-id
    C5.S2.E3.m2adec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
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    Q11279
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C5.S1.XMD4.m1adec
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    Q11273
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C5.S1.XMD7.m1adec
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