DLMF:19.16.E9 (Q6324): Difference between revisions

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Changed an Item: Wikidata Toolkit example test statement addition
Changed an Item: Add constraint
Property / constraint
 

b j subscript 𝑏 𝑗 {\displaystyle{\displaystyle b_{j}\in\mathbb{R}}}

b_{j}\in\Reals
Property / constraint: b j subscript 𝑏 𝑗 {\displaystyle{\displaystyle b_{j}\in\mathbb{R}}} / rank
 
Normal rank

Revision as of 18:06, 30 December 2019

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DLMF:19.16.E9
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    Statements

    R - a ( 𝐛 ; 𝐳 ) = 1 B ( a , a ) 0 t a - 1 j = 1 n ( t + z j ) - b j d t = 1 B ( a , a ) 0 t a - 1 j = 1 n ( 1 + t z j ) - b j d t , Carlson-integral-R 𝑎 𝐛 𝐳 1 Euler-Beta 𝑎 superscript 𝑎 superscript subscript 0 superscript 𝑡 superscript 𝑎 1 subscript superscript product 𝑛 𝑗 1 superscript 𝑡 subscript 𝑧 𝑗 subscript 𝑏 𝑗 𝑡 1 Euler-Beta 𝑎 superscript 𝑎 superscript subscript 0 superscript 𝑡 𝑎 1 subscript superscript product 𝑛 𝑗 1 superscript 1 𝑡 subscript 𝑧 𝑗 subscript 𝑏 𝑗 𝑡 {\displaystyle{\displaystyle R_{-a}\left(\mathbf{b};\mathbf{z}\right)=\frac{1}% {\mathrm{B}\left(a,a^{\prime}\right)}\int_{0}^{\infty}t^{a^{\prime}-1}\prod^{n% }_{j=1}(t+z_{j})^{-b_{j}}\mathrm{d}t=\frac{1}{\mathrm{B}\left(a,a^{\prime}% \right)}\int_{0}^{\infty}t^{a-1}\prod^{n}_{j=1}(1+tz_{j})^{-b_{j}}\mathrm{d}t,}}
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    DLMF:19.16.E9
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    b j subscript 𝑏 𝑗 {\displaystyle{\displaystyle b_{j}\in\mathbb{R}}}
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