DLMF:5.13.E2 (Q2159): 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.m2aadec

Revision as of 00:04, 2 January 2020

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DLMF:5.13.E2
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    Statements

    1 2 π - | Γ ( a + i t ) | 2 e ( 2 b - π ) t d t = Γ ( 2 a ) ( 2 sin b ) 2 a , 1 2 𝜋 superscript subscript superscript Euler-Gamma 𝑎 𝑖 𝑡 2 superscript 𝑒 2 𝑏 𝜋 𝑡 𝑡 Euler-Gamma 2 𝑎 superscript 2 𝑏 2 𝑎 {\displaystyle{\displaystyle{\frac{1}{2\pi}\int_{-\infty}^{\infty}|\Gamma\left% (a+it\right)|^{2}e^{(2b-\pi)t}\mathrm{d}t=\frac{\Gamma\left(2a\right)}{(2\sin b% )^{2a}}},}}
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    0 < b < π 0 𝑏 𝜋 {\displaystyle{\displaystyle 0<b<\pi}}
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    Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    C5.S2.E1.m2aadec
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aadec
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