DLMF:5.11.E3 (Q2119)

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DLMF:5.11.E3
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    Statements

    Defining formula
    Γ ⁡ ( z ) ∼ e - z ⁢ z z ⁢ ( 2 ⁢ π z ) 1 / 2 ⁢ ∑ k = 0 ∞ g k z k , asymptotic-expansion Euler-Gamma 𝑧 𝑧 superscript 𝑧 𝑧 superscript 2 𝜋 𝑧 1 2 superscript subscript 𝑘 0 subscript 𝑔 𝑘 superscript 𝑧 𝑘 {\displaystyle{\displaystyle\Gamma\left(z\right)\sim{\mathrm{e}^{-z}}z^{z}% \left(\frac{2\pi}{z}\right)^{1/2}\sum_{k=0}^{\infty}\frac{g_{k}}{z^{k}},}}
    0 references
    DLMF id
    DLMF:5.11.E3
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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
    0 references
     
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