DLMF:12.10.E16 (Q4174)

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DLMF:12.10.E16
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    Statements

    Defining formula
    Γ ⁡ ( 1 2 + z ) ∼ 2 ⁢ π ⁢ e - z ⁢ z z ⁢ ∑ s = 0 ∞ γ s z s ; asymptotic-expansion Euler-Gamma 1 2 𝑧 2 𝜋 superscript 𝑒 𝑧 superscript 𝑧 𝑧 superscript subscript 𝑠 0 subscript 𝛾 𝑠 superscript 𝑧 𝑠 {\displaystyle{\displaystyle\Gamma\left(\tfrac{1}{2}+z\right)\sim\sqrt{2\pi}e^% {-z}z^{z}\sum_{s=0}^{\infty}\frac{\gamma_{s}}{z^{s}};}}
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    DLMF id
    DLMF:12.10.E16
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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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    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11aedec
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aedec
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