DLMF:8.10.E3 (Q2556)

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DLMF:8.10.E3
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    Statements

    Defining formula
    x 1 - a ⁢ e x ⁢ Γ ⁡ ( a , x ) = 1 + a - 1 x ⁢ ϑ , superscript 𝑥 1 𝑎 superscript 𝑒 𝑥 incomplete-Gamma 𝑎 𝑥 1 𝑎 1 𝑥 italic-ϑ {\displaystyle{\displaystyle x^{1-a}e^{x}\Gamma\left(a,x\right)=1+\frac{a-1}{x% }\vartheta,}}
    0 references
    DLMF id
    DLMF:8.10.E3
    0 references
    Symbols used
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
    0 references
    incomplete gamma function
    Defining formula
    Γ ⁡ ( a , z ) incomplete-Gamma 𝑎 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C8.S2.E2.m2aadec
    0 references
    Q11332
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C8.S1.XMD1.m1bdec
    0 references
    Q11324
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C8.S1.XMD3.m1bdec
    0 references
     
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