DLMF:12.10.E16 (Q4174): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
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
 
Defining formula:

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.m2adec

Revision as of 15:18, 2 January 2020

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DLMF:12.10.E16
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    Statements

    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:12.10.E16
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    Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    C5.S2.E1.m2abdec
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    asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    C2.S1.SS3.p1.m11aedec
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2adec
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