DLMF:5.9.E5 (Q2094): Difference between revisions

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imported>Admin
Property / constraint
 

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

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

Revision as of 16:04, 30 December 2019

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DLMF:5.9.E5
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    Γ ( z ) = 0 t z - 1 ( e - t - k = 0 n ( - 1 ) k t k k ! ) d t , Euler-Gamma 𝑧 superscript subscript 0 superscript 𝑡 𝑧 1 superscript 𝑒 𝑡 superscript subscript 𝑘 0 𝑛 superscript 1 𝑘 superscript 𝑡 𝑘 𝑘 𝑡 {\displaystyle{\displaystyle\Gamma\left(z\right)=\int_{0}^{\infty}t^{z-1}\left% (e^{-t}-\sum_{k=0}^{n}\frac{(-1)^{k}t^{k}}{k!}\right)\mathrm{d}t,}}
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    - n - 1 < z < - n 𝑛 1 𝑧 𝑛 {\displaystyle{\displaystyle-n-1<\Re z<-n}}
    0 references