DLMF:5.6.E9 (Q2076)

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DLMF:5.6.E9
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    Statements

    Defining formula
    | Γ ⁡ ( z ) | ≤ ( 2 ⁢ π ) 1 / 2 ⁢ | z | x - ( 1 / 2 ) ⁢ e - π ⁢ | y | / 2 ⁢ exp ⁡ ( 1 6 ⁢ | z | - 1 ) . Euler-Gamma 𝑧 superscript 2 𝜋 1 2 superscript 𝑧 𝑥 1 2 superscript 𝑒 𝜋 𝑦 2 1 6 superscript 𝑧 1 {\displaystyle{\displaystyle|\Gamma\left(z\right)|\leq(2\pi)^{1/2}|z|^{x-(1/2)% }e^{-\pi|y|/2}\exp\left(\tfrac{1}{6}|z|^{-1}\right).}}
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    DLMF id
    DLMF:5.6.E9
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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.m2ahdec
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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.m2abdec
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    exponential function
    Defining formula
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2aadec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
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    Q11281
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C5.S1.XMD5.m1gdec
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    Q11278
    Defining formula
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C5.S1.XMD6.m1bdec
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    Q11273
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C5.S1.XMD7.m1adec
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