DLMF:15.14.E1 (Q5176): Difference between revisions

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Property / constraint
 

min ( a , b ) > s > 0 𝑎 𝑏 𝑠 0 {\displaystyle{\displaystyle\min(\Re a,\Re b)>\Re s>0}}

\min(\realpart@@{a},\realpart@@{b})>\realpart@@{s}>0
Property / constraint: min ( a , b ) > s > 0 𝑎 𝑏 𝑠 0 {\displaystyle{\displaystyle\min(\Re a,\Re b)>\Re s>0}} / rank
 
Normal rank

Revision as of 17:57, 30 December 2019

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DLMF:15.14.E1
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    0 x s - 1 𝐅 ( a , b c ; - x ) d x = Γ ( s ) Γ ( a - s ) Γ ( b - s ) Γ ( a ) Γ ( b ) Γ ( c - s ) , superscript subscript 0 superscript 𝑥 𝑠 1 scaled-hypergeometric-bold-F 𝑎 𝑏 𝑐 𝑥 𝑥 Euler-Gamma 𝑠 Euler-Gamma 𝑎 𝑠 Euler-Gamma 𝑏 𝑠 Euler-Gamma 𝑎 Euler-Gamma 𝑏 Euler-Gamma 𝑐 𝑠 {\displaystyle{\displaystyle\int_{0}^{\infty}x^{s-1}\mathbf{F}\left({a,b\atop c% };-x\right)\mathrm{d}x=\frac{\Gamma\left(s\right)\Gamma\left(a-s\right)\Gamma% \left(b-s\right)}{\Gamma\left(a\right)\Gamma\left(b\right)\Gamma\left(c-s% \right)},}}
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    DLMF:15.14.E1
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    min ( a , b ) > s > 0 𝑎 𝑏 𝑠 0 {\displaystyle{\displaystyle\min(\Re a,\Re b)>\Re s>0}}
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