Formula:KLS:09.12:10

<< Formula:KLS:09.12:09

formula in Laguerre

Formula:KLS:09.12:11 >>

${\displaystyle{\displaystyle{\displaystyle{\mathrm{e}^{-x}}x^{\alpha}L^{\alpha}_{n}\left(x\right)=\frac{1}{n!}\left(\frac{d}{dx}\right)^{n}\left[{\mathrm{e}^{-x}}x^{n+\alpha}\right]}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle\mathrm{e}}}}$ : the base of the natural logarithm : http://dlmf.nist.gov/4.2.E11
${\displaystyle{\displaystyle{\displaystyle L_{n}^{(\alpha)}}}}$ : Laguerre (or generalized Laguerre) polynomial : http://dlmf.nist.gov/18.3#T1.t1.r27

Bibliography

Equation in Section 9.12 of KLS.

URL links

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<< Formula:KLS:09.12:09

formula in Laguerre

Formula:KLS:09.12:11 >>