DLMF:8.7.E1 (Q2527)

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DLMF:8.7.E1
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    Statements

    Defining formula
    γ * ⁡ ( a , z ) = e - z ⁢ ∑ k = 0 ∞ z k Γ ⁡ ( a + k + 1 ) = 1 Γ ⁡ ( a ) ⁢ ∑ k = 0 ∞ ( - z ) k k ! ⁢ ( a + k ) . incomplete-gamma-star 𝑎 𝑧 superscript 𝑒 𝑧 superscript subscript 𝑘 0 superscript 𝑧 𝑘 Euler-Gamma 𝑎 𝑘 1 1 Euler-Gamma 𝑎 superscript subscript 𝑘 0 superscript 𝑧 𝑘 𝑘 𝑎 𝑘 {\displaystyle{\displaystyle\gamma^{*}\left(a,z\right)=e^{-z}\sum_{k=0}^{% \infty}\frac{z^{k}}{\Gamma\left(a+k+1\right)}=\frac{1}{\Gamma\left(a\right)}% \sum_{k=0}^{\infty}\frac{(-z)^{k}}{k!(a+k)}.}}
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    DLMF id
    DLMF:8.7.E1
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