DLMF:8.7.E2 (Q2528)

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DLMF:8.7.E2
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    Statements

    Defining formula
    γ ⁡ ( a , x + y ) - γ ⁡ ( a , x ) = Γ ⁡ ( a , x ) - Γ ⁡ ( a , x + y ) = e - x ⁢ x a - 1 ⁢ ∑ n = 0 ∞ ( 1 - a ) n ( - x ) n ⁢ ( 1 - e - y ⁢ e n ⁢ ( y ) ) , incomplete-gamma 𝑎 𝑥 𝑦 incomplete-gamma 𝑎 𝑥 incomplete-Gamma 𝑎 𝑥 incomplete-Gamma 𝑎 𝑥 𝑦 superscript 𝑒 𝑥 superscript 𝑥 𝑎 1 superscript subscript 𝑛 0 Pochhammer 1 𝑎 𝑛 superscript 𝑥 𝑛 1 superscript 𝑒 𝑦 subscript 𝑒 𝑛 𝑦 {\displaystyle{\displaystyle\gamma\left(a,x+y\right)-\gamma\left(a,x\right)=% \Gamma\left(a,x\right)-\Gamma\left(a,x+y\right)=e^{-x}x^{a-1}\sum_{n=0}^{% \infty}\frac{{\left(1-a\right)_{n}}}{(-x)^{n}}(1-e^{-y}e_{n}(y)),}}
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    DLMF id
    DLMF:8.7.E2
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    constraint
    | y | < | x | 𝑦 𝑥 {\displaystyle{\displaystyle|y|<|x|}}
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