DLMF:16.5.E3 (Q5214): Difference between revisions

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Property / constraint
 

z < 1 𝑧 1 {\displaystyle{\displaystyle\Re z<1}}

\realpart@@{z}<1
Property / constraint: z < 1 𝑧 1 {\displaystyle{\displaystyle\Re z<1}} / rank
 
Normal rank

Revision as of 17:57, 30 December 2019

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DLMF:16.5.E3
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    Statements

    F q p + 1 ( a 0 , , a p b 1 , , b q ; z ) = 1 Γ ( a 0 ) 0 e - t t a 0 - 1 F q p ( a 1 , , a p b 1 , , b q ; z t ) d t , Gauss-hypergeometric-pFq 𝑝 1 𝑞 subscript 𝑎 0 subscript 𝑎 𝑝 subscript 𝑏 1 subscript 𝑏 𝑞 𝑧 1 Euler-Gamma subscript 𝑎 0 superscript subscript 0 𝑡 superscript 𝑡 subscript 𝑎 0 1 Gauss-hypergeometric-pFq 𝑝 𝑞 subscript 𝑎 1 subscript 𝑎 𝑝 subscript 𝑏 1 subscript 𝑏 𝑞 𝑧 𝑡 𝑡 {\displaystyle{\displaystyle{{}_{p+1}F_{q}}\left({a_{0},\dots,a_{p}\atop b_{1}% ,\dots,b_{q}};z\right)=\frac{1}{\Gamma\left(a_{0}\right)}\int_{0}^{\infty}{% \mathrm{e}^{-t}}t^{a_{0}-1}{{}_{p}F_{q}}\left({a_{1},\dots,a_{p}\atop b_{1},% \cdots,b_{q}};zt\right)\mathrm{d}t,}}
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    DLMF:16.5.E3
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    z < 1 𝑧 1 {\displaystyle{\displaystyle\Re z<1}}
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