DLMF:18.17.E38 (Q5779): Difference between revisions

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Created a new Item: Wikidata Toolkit example test item creation
 
Changed an Item: Add constraint
Property / constraint
 

z > 0 𝑧 0 {\displaystyle{\displaystyle\Re z>0}}

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

Revision as of 18:02, 30 December 2019

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DLMF:18.17.E38
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    0 1 P 2 n ( x ) x z - 1 d x = ( - 1 ) n ( 1 2 - 1 2 z ) n 2 ( 1 2 z ) n + 1 , superscript subscript 0 1 Legendre-spherical-polynomial 2 𝑛 𝑥 superscript 𝑥 𝑧 1 𝑥 superscript 1 𝑛 Pochhammer 1 2 1 2 𝑧 𝑛 2 Pochhammer 1 2 𝑧 𝑛 1 {\displaystyle{\displaystyle\int_{0}^{1}P_{2n}\left(x\right)x^{z-1}\mathrm{d}x% =\frac{(-1)^{n}{\left(\frac{1}{2}-\frac{1}{2}z\right)_{n}}}{2{\left(\frac{1}{2% }z\right)_{n+1}}},}}
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    DLMF:18.17.E38
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    z > 0 𝑧 0 {\displaystyle{\displaystyle\Re z>0}}
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