DLMF:8.7.E6 (Q2532)

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DLMF:8.7.E6
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    Statements

    test
    Γ ⁡ ( a , x ) = x a ⁢ e - x ⁢ ∑ n = 0 ∞ L n ( a ) ⁡ ( x ) n + 1 , incomplete-Gamma 𝑎 𝑥 superscript 𝑥 𝑎 superscript 𝑒 𝑥 superscript subscript 𝑛 0 Laguerre-polynomial-L 𝑎 𝑛 𝑥 𝑛 1 {\displaystyle{\displaystyle\Gamma\left(a,x\right)=x^{a}e^{-x}\sum_{n=0}^{% \infty}\frac{L^{(a)}_{n}\left(x\right)}{n+1},}}
    0 references
    DLMF id
    DLMF:8.7.E6
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    constraint
    x > 0 𝑥 0 {\displaystyle{\displaystyle x>0}}
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    Symbols used
    Q11333
    test
    L n ( α ) ⁡ ( x ) Laguerre-polynomial-L 𝛼 𝑛 𝑥 {\displaystyle{\displaystyle L^{(\NVar{\alpha})}_{\NVar{n}}\left(\NVar{x}% \right)}}
    xml-id
    C18.S3.T1.t1.r12.m2adec
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    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aedec
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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.E2.m2abdec
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    Q11332
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C8.S1.XMD1.m1bdec
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    Q11324
    test
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C8.S1.XMD3.m1edec
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    Q11329
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C8.S1.XMD6.m1cdec
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