DLMF:8.6.E4 (Q2518): Difference between revisions

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Property / constraint
 

a < 1 𝑎 1 {\displaystyle{\displaystyle\Re a<1}}

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

Revision as of 16:09, 30 December 2019

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DLMF:8.6.E4
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    Statements

    Γ ( a , z ) = z a e - z Γ ( 1 - a ) 0 t - a e - t z + t d t , incomplete-Gamma 𝑎 𝑧 superscript 𝑧 𝑎 superscript 𝑒 𝑧 Euler-Gamma 1 𝑎 superscript subscript 0 superscript 𝑡 𝑎 superscript 𝑒 𝑡 𝑧 𝑡 𝑡 {\displaystyle{\displaystyle\Gamma\left(a,z\right)=\frac{z^{a}e^{-z}}{\Gamma% \left(1-a\right)}\int_{0}^{\infty}\frac{t^{-a}e^{-t}}{z+t}\mathrm{d}t,}}
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    | ph z | < π phase 𝑧 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|<\pi}}
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    a < 1 𝑎 1 {\displaystyle{\displaystyle\Re a<1}}
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