DLMF:8.8.E11 (Q2543)

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DLMF:8.8.E11
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    Statements

    Defining formula
    P ⁡ ( a + n , z ) = P ⁡ ( a , z ) - z a ⁢ e - z ⁢ ∑ k = 0 n - 1 z k Γ ⁡ ( a + k + 1 ) , incomplete-gamma-P 𝑎 𝑛 𝑧 incomplete-gamma-P 𝑎 𝑧 superscript 𝑧 𝑎 superscript 𝑒 𝑧 superscript subscript 𝑘 0 𝑛 1 superscript 𝑧 𝑘 Euler-Gamma 𝑎 𝑘 1 {\displaystyle{\displaystyle P\left(a+n,z\right)=P\left(a,z\right)-z^{a}e^{-z}% \sum_{k=0}^{n-1}\frac{z^{k}}{\Gamma\left(a+k+1\right)},}}
    0 references
    DLMF id
    DLMF:8.8.E11
    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.m2agdec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aidec
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    Q11325
    Defining formula
    P ⁡ ( a , z ) incomplete-gamma-P 𝑎 𝑧 {\displaystyle{\displaystyle P\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C8.S2.E4.m1aadec
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    Q11323
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C8.S1.XMD2.m1jdec
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    Q11324
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C8.S1.XMD3.m1jdec
    0 references
     
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