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

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Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
test:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2aedec

Revision as of 16:03, 1 January 2020

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DLMF:2.5.E14
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    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
     
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