DLMF:8.7.E3 (Q2529): Difference between revisions

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Property / constraint
 

a 0 , - 1 , - 2 , 𝑎 0 1 2 {\displaystyle{\displaystyle a\neq 0,-1,-2,\dots}}

a\neq 0,-1,-2,\dots
Property / constraint: a 0 , - 1 , - 2 , 𝑎 0 1 2 {\displaystyle{\displaystyle a\neq 0,-1,-2,\dots}} / rank
 
Normal rank

Revision as of 16:10, 30 December 2019

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DLMF:8.7.E3
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    Γ ( a , z ) = Γ ( a ) - k = 0 ( - 1 ) k z a + k k ! ( a + k ) = Γ ( a ) ( 1 - z a e - z k = 0 z k Γ ( a + k + 1 ) ) , incomplete-Gamma 𝑎 𝑧 Euler-Gamma 𝑎 superscript subscript 𝑘 0 superscript 1 𝑘 superscript 𝑧 𝑎 𝑘 𝑘 𝑎 𝑘 Euler-Gamma 𝑎 1 superscript 𝑧 𝑎 superscript 𝑒 𝑧 superscript subscript 𝑘 0 superscript 𝑧 𝑘 Euler-Gamma 𝑎 𝑘 1 {\displaystyle{\displaystyle\Gamma\left(a,z\right)=\Gamma\left(a\right)-\sum_{% k=0}^{\infty}\frac{(-1)^{k}z^{a+k}}{k!(a+k)}=\Gamma\left(a\right)\left(1-z^{a}% e^{-z}\sum_{k=0}^{\infty}\frac{z^{k}}{\Gamma\left(a+k+1\right)}\right),}}
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    a 0 , - 1 , - 2 , 𝑎 0 1 2 {\displaystyle{\displaystyle a\neq 0,-1,-2,\dots}}
    0 references