DLMF:18.9.E24 (Q5620)

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DLMF:18.9.E24
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    Statements

    test
    d d x ⁡ ( e - x ⁢ x α ⁢ L n ( α ) ⁡ ( x ) ) = ( n + 1 ) ⁢ e - x ⁢ x α - 1 ⁢ L n + 1 ( α - 1 ) ⁡ ( x ) . derivative 𝑥 superscript 𝑒 𝑥 superscript 𝑥 𝛼 Laguerre-polynomial-L 𝛼 𝑛 𝑥 𝑛 1 superscript 𝑒 𝑥 superscript 𝑥 𝛼 1 Laguerre-polynomial-L 𝛼 1 𝑛 1 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}}{\mathrm{d}x}\left(e^{-x}x^{% \alpha}L^{(\alpha)}_{n}\left(x\right)\right)=(n+1)e^{-x}x^{\alpha-1}L^{(\alpha% -1)}_{n+1}\left(x\right).}}
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    DLMF id
    DLMF:18.9.E24
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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.m2addec
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    derivative of $$f$$ with respect to $$x$$
    test
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    xml-id
    C1.S4.E4.m2aidec
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    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
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    Q11726
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1xdec
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    Q11727
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1wdec
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