DLMF:5.12.E10 (Q2155): Difference between revisions

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Property / constraint
 

a > 0 𝑎 0 {\displaystyle{\displaystyle\Re a>0}}

\realpart@@{a}>0
Property / constraint: a > 0 𝑎 0 {\displaystyle{\displaystyle\Re a>0}} / rank
 
Normal rank

Revision as of 16:05, 30 December 2019

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DLMF:5.12.E10
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    Statements

    1 2 π i 0 ( 1 + ) t a - 1 ( t - 1 ) b - 1 d t = sin ( π b ) π B ( a , b ) , 1 2 𝜋 𝑖 superscript subscript 0 limit-from 1 superscript 𝑡 𝑎 1 superscript 𝑡 1 𝑏 1 𝑡 𝜋 𝑏 𝜋 Euler-Beta 𝑎 𝑏 {\displaystyle{\displaystyle{\frac{1}{2\pi i}\int_{0}^{(1+)}t^{a-1}(t-1)^{b-1}% \mathrm{d}t=\frac{\sin\left(\pi b\right)}{\pi}\mathrm{B}\left(a,b\right)},}}
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    a > 0 𝑎 0 {\displaystyle{\displaystyle\Re a>0}}
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