DLMF:8.6.E9 (Q2523): Difference between revisions

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Property / constraint
 

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

\realpart@@{z}>0
Property / constraint: z > 0 𝑧 0 {\displaystyle{\displaystyle\Re z>0}} / rank
 
Normal rank

Revision as of 16:09, 30 December 2019

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DLMF:8.6.E9
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    Statements

    Γ ( - a , z e ± π i ) = e z e π i a Γ ( 1 + a ) 0 t a e - z t t - 1 d t , incomplete-Gamma 𝑎 𝑧 superscript 𝑒 plus-or-minus 𝜋 𝑖 superscript 𝑒 𝑧 superscript 𝑒 minus-or-plus 𝜋 imaginary-unit 𝑎 Euler-Gamma 1 𝑎 superscript subscript 0 superscript 𝑡 𝑎 superscript 𝑒 𝑧 𝑡 𝑡 1 𝑡 {\displaystyle{\displaystyle\Gamma\left(-a,ze^{\pm\pi i}\right)=\frac{e^{z}e^{% \mp\pi\mathrm{i}a}}{\Gamma\left(1+a\right)}\int_{0}^{\infty}\frac{t^{a}e^{-zt}% }{t-1}\mathrm{d}t,}}
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    z > 0 𝑧 0 {\displaystyle{\displaystyle\Re z>0}}
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