DLMF:5.12.E9 (Q2154): Difference between revisions

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Property / constraint
 

0 < c < 1 0 𝑐 1 {\displaystyle{\displaystyle 0<c<1}}

0<c<1
Property / constraint: 0 < c < 1 0 𝑐 1 {\displaystyle{\displaystyle 0<c<1}} / rank
 
Normal rank

Revision as of 16:05, 30 December 2019

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DLMF:5.12.E9
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    Statements

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