DLMF:8.8.E7 (Q2539)

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DLMF:8.8.E7
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    Statements

    Defining formula
    γ ⁡ ( a + n , z ) = ( a ) n ⁢ γ ⁡ ( a , z ) - z a ⁢ e - z ⁢ ∑ k = 0 n - 1 Γ ⁡ ( a + n ) Γ ⁡ ( a + k + 1 ) ⁢ z k , incomplete-gamma 𝑎 𝑛 𝑧 Pochhammer 𝑎 𝑛 incomplete-gamma 𝑎 𝑧 superscript 𝑧 𝑎 superscript 𝑒 𝑧 superscript subscript 𝑘 0 𝑛 1 Euler-Gamma 𝑎 𝑛 Euler-Gamma 𝑎 𝑘 1 superscript 𝑧 𝑘 {\displaystyle{\displaystyle\gamma\left(a+n,z\right)={\left(a\right)_{n}}% \gamma\left(a,z\right)-z^{a}e^{-z}\sum_{k=0}^{n-1}\frac{\Gamma\left(a+n\right)% }{\Gamma\left(a+k+1\right)}z^{k},}}
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    DLMF id
    DLMF:8.8.E7
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