DLMF:18.17.E15 (Q5756)

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DLMF:18.17.E15
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    Statements

    test
    e - x ⁢ L n ( α ) ⁡ ( x ) = ∫ x ∞ e - y ⁢ L n ( α + μ ) ⁡ ( y ) ⁢ ( y - x ) μ - 1 Γ ⁡ ( μ ) ⁢ d y , superscript 𝑒 𝑥 Laguerre-polynomial-L 𝛼 𝑛 𝑥 superscript subscript 𝑥 superscript 𝑒 𝑦 Laguerre-polynomial-L 𝛼 𝜇 𝑛 𝑦 superscript 𝑦 𝑥 𝜇 1 Euler-Gamma 𝜇 𝑦 {\displaystyle{\displaystyle e^{-x}L^{(\alpha)}_{n}\left(x\right)=\int_{x}^{% \infty}e^{-y}L^{(\alpha+\mu)}_{n}\left(y\right)\frac{(y-x)^{\mu-1}}{\Gamma% \left(\mu\right)}\mathrm{d}y,}}
    0 references
    DLMF id
    DLMF:18.17.E15
    0 references
    constraint
    μ > 0 𝜇 0 {\displaystyle{\displaystyle\mu>0}}
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2agdec
    0 references
    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.m2aadec
    0 references
     
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