DLMF:19.16.E24 (Q6342): Difference between revisions

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Property / constraint
 

a + a > b 1 > 0 𝑎 superscript 𝑎 subscript 𝑏 1 0 {\displaystyle{\displaystyle a+a^{\prime}>b_{1}>0}}

a+a^{\prime}>b_{1}>0
Property / constraint: a + a > b 1 > 0 𝑎 superscript 𝑎 subscript 𝑏 1 0 {\displaystyle{\displaystyle a+a^{\prime}>b_{1}>0}} / rank
 
Normal rank

Revision as of 18:06, 30 December 2019

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DLMF:19.16.E24
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    R - a ( 𝐛 ; 𝐳 ) = z 1 a - b 1 B ( b 1 , a - b 1 ) 0 t b 1 - 1 ( t + z 1 ) - a R - a ( 𝐛 ; 0 , t + z 2 , , t + z n ) d t , Carlson-integral-R 𝑎 𝐛 𝐳 superscript subscript 𝑧 1 superscript 𝑎 subscript 𝑏 1 Euler-Beta subscript 𝑏 1 superscript 𝑎 subscript 𝑏 1 superscript subscript 0 superscript 𝑡 subscript 𝑏 1 1 superscript 𝑡 subscript 𝑧 1 superscript 𝑎 Carlson-integral-R 𝑎 𝐛 0 𝑡 subscript 𝑧 2 𝑡 subscript 𝑧 𝑛 𝑡 {\displaystyle{\displaystyle R_{-a}\left(\mathbf{b};\mathbf{z}\right)=\frac{z_% {1}^{a^{\prime}-b_{1}}}{\mathrm{B}\left(b_{1},a^{\prime}-b_{1}\right)}\int_{0}% ^{\infty}t^{b_{1}-1}(t+z_{1})^{-a^{\prime}}\*R_{-a}\left(\mathbf{b};0,t+z_{2},% \dots,t+z_{n}\right)\mathrm{d}t,}}
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    DLMF:19.16.E24
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    a + a > b 1 > 0 𝑎 superscript 𝑎 subscript 𝑏 1 0 {\displaystyle{\displaystyle a+a^{\prime}>b_{1}>0}}
    0 references