DLMF:2.5.E14 (Q790): Difference between revisions

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imported>Admin
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
test:

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2acdec

Revision as of 16:03, 1 January 2020

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DLMF:2.5.E14
No description defined

    Statements

    test
    | Γ ⁡ ( x + i ⁢ y ) | = 2 ⁢ π ⁢ e - π ⁢ | y | / 2 ⁢ | y | x - ( 1 / 2 ) ⁢ ( 1 + o ⁡ ( 1 ) ) , Euler-Gamma 𝑥 𝑖 𝑦 2 𝜋 superscript 𝑒 𝜋 𝑦 2 superscript 𝑦 𝑥 1 2 1 little-o 1 {\displaystyle{\displaystyle|\Gamma\left(x+iy\right)|=\sqrt{2\pi}e^{-\pi|y|/2}% |y|^{x-(1/2)}\left(1+o\left(1\right)\right),}}
    0 references
    DLMF id
    DLMF:2.5.E14
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2abdec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aedec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2acdec
    0 references
     
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