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DLMF:5.6.E6 - MaRDI portal

DLMF:5.6.E6 (Q2627)

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DLMF:5.6.E6
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    Statements

    DLMF defining formula
    | Γ ⁡ ( x + i ⁢ y ) | ≤ | Γ ⁡ ( x ) | , Euler-Gamma 𝑥 imaginary-unit 𝑦 Euler-Gamma 𝑥 {\displaystyle{\displaystyle|\Gamma\left(x+\mathrm{i}y\right)|\leq|\Gamma\left% (x\right)|,}}
    0 references
    Symbols used
    gamma function
    DLMF defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aedec
    0 references
    imaginary unit
    DLMF defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C5.S1.XMD5.m1edec
    0 references
    real variable
    DLMF defining formula
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C5.S1.XMD6.m1dec
    0 references

    Identifiers

     
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