DLMF:8.8.E10 (Q2542)

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DLMF:8.8.E10
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    Statements

    Defining formula
    Γ ⁡ ( a , z ) = Γ ⁡ ( a ) Γ ⁡ ( a - n ) ⁢ Γ ⁡ ( a - n , z ) + z a - 1 ⁢ e - z ⁢ ∑ k = 0 n - 1 Γ ⁡ ( a ) Γ ⁡ ( a - k ) ⁢ z - k , incomplete-Gamma 𝑎 𝑧 Euler-Gamma 𝑎 Euler-Gamma 𝑎 𝑛 incomplete-Gamma 𝑎 𝑛 𝑧 superscript 𝑧 𝑎 1 superscript 𝑒 𝑧 superscript subscript 𝑘 0 𝑛 1 Euler-Gamma 𝑎 Euler-Gamma 𝑎 𝑘 superscript 𝑧 𝑘 {\displaystyle{\displaystyle\Gamma\left(a,z\right)=\frac{\Gamma\left(a\right)}% {\Gamma\left(a-n\right)}\Gamma\left(a-n,z\right)+z^{a-1}e^{-z}\sum_{k=0}^{n-1}% \frac{\Gamma\left(a\right)}{\Gamma\left(a-k\right)}z^{-k},}}
    0 references
    DLMF id
    DLMF:8.8.E10
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2afdec
    0 references
     
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