DLMF:18.17.E34 (Q5775)

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DLMF:18.17.E34
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    test
    ∫ 0 ∞ e - x ⁢ z ⁢ L n ( α ) ⁡ ( x ) ⁢ e - x ⁢ x α ⁢ d x = Γ ⁡ ( α + n + 1 ) ⁢ z n n ! ⁢ ( z + 1 ) α + n + 1 , superscript subscript 0 superscript 𝑒 𝑥 𝑧 Laguerre-polynomial-L 𝛼 𝑛 𝑥 superscript 𝑒 𝑥 superscript 𝑥 𝛼 𝑥 Euler-Gamma 𝛼 𝑛 1 superscript 𝑧 𝑛 𝑛 superscript 𝑧 1 𝛼 𝑛 1 {\displaystyle{\displaystyle\int_{0}^{\infty}e^{-xz}L^{(\alpha)}_{n}\left(x% \right)e^{-x}x^{\alpha}\mathrm{d}x=\frac{\Gamma\left(\alpha+n+1\right)z^{n}}{n% !(z+1)^{\alpha+n+1}},}}
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    DLMF id
    DLMF:18.17.E34
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