DLMF:13.10.E7 (Q4466): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:13.10.E7	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{0}^{\infty}e^{-zt}t^{b-1}U\left(a,c,t\right)% \mathrm{d}t=\Gamma\left(b\right)\Gamma\left(b-c+1\right)\*z^{-b}{{}_{2}{% \mathbf{F}}_{1}}\left(a,b;a+b-c+1;1-\frac{1}{z}\right),}}

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DLMF:13.10.E7

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{\displaystyle{\displaystyle\Re b>\max\left(\Re c-1,0\right)}}

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

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Defining formula

{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

C5.S2.E1.m2acdec

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Kummer confluent hypergeometric function

Defining formula

{\displaystyle{\displaystyle U\left(\NVar{a},\NVar{b},\NVar{z}\right)}}

C13.S2.E6.m2abdec

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Defining formula

{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

C1.S4.SS4.m1afdec

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base of natural logarithm

Defining formula

{\displaystyle{\displaystyle\mathrm{e}}}

C4.S2.E11.m2addec

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scaled (or Olver’s) generalized hypergeometric function

Defining formula

{\displaystyle{\displaystyle{{}_{\NVar{p}}{\mathbf{F}}_{\NVar{q}}}\left(\NVar{% \mathbf{a}};\NVar{\mathbf{b}};\right)\)\@add@PDF@RDFa@triples\end{document}}}

C16.S2.E5.m2aadec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3afdec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1addec

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Defining formula

{\displaystyle{\displaystyle z}}

C13.S1.XMD6.m1edec

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Sitelinks

Wikipedia(0 entries)

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