DLMF:5.12.E6 (Q2151): Difference between revisions

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Created a new Item: Wikidata Toolkit example test item creation
 
Changed an Item: Add constraint
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 17:05, 30 December 2019

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DLMF:5.12.E6
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    0 π ( sin t ) a - 1 e i b t d t = π 2 a - 1 e i π b / 2 a B ( 1 2 ( a + b + 1 ) , 1 2 ( a - b + 1 ) ) , superscript subscript 0 𝜋 superscript 𝑡 𝑎 1 superscript 𝑒 𝑖 𝑏 𝑡 𝑡 𝜋 superscript 2 𝑎 1 superscript 𝑒 𝑖 𝜋 𝑏 2 𝑎 Euler-Beta 1 2 𝑎 𝑏 1 1 2 𝑎 𝑏 1 {\displaystyle{\displaystyle\int_{0}^{\pi}(\sin t)^{a-1}e^{ibt}\mathrm{d}t=% \frac{\pi}{2^{a-1}}\frac{e^{i\pi b/2}}{a\mathrm{B}\left(\frac{1}{2}(a+b+1),% \frac{1}{2}(a-b+1)\right)},}}
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    DLMF:5.12.E6
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    a > 0 𝑎 0 {\displaystyle{\displaystyle\Re a>0}}
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