DLMF:8.11.E4 (Q2575)

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DLMF:8.11.E4
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    Statements

    test
    γ ⁡ ( a , z ) = z a ⁢ e - z ⁢ ∑ k = 0 ∞ z k ( a ) k + 1 , incomplete-gamma 𝑎 𝑧 superscript 𝑧 𝑎 superscript 𝑒 𝑧 superscript subscript 𝑘 0 superscript 𝑧 𝑘 Pochhammer 𝑎 𝑘 1 {\displaystyle{\displaystyle\gamma\left(a,z\right)=z^{a}e^{-z}\sum_{k=0}^{% \infty}\frac{z^{k}}{{\left(a\right)_{k+1}}},}}
    0 references
    DLMF id
    DLMF:8.11.E4
    0 references
    constraint
    a ≠ 0 , - 1 , - 2 , … 𝑎 0 1 2 … {\displaystyle{\displaystyle a\neq 0,-1,-2,\dots}}
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    Symbols used
    Q10759
    test
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1aadec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
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    incomplete gamma function
    test
    γ ⁡ ( a , z ) incomplete-gamma 𝑎 𝑧 {\displaystyle{\displaystyle\gamma\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C8.S2.E1.m2adec
    0 references
    Q11323
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C8.S1.XMD2.m1bdec
    0 references
     
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