Formula:KLS:09.12:29

<< Formula:KLS:09.12:28

formula in Laguerre

Formula:KLS:09.12:30 >>

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

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:09.12:28

formula in Laguerre

Formula:KLS:09.12:30 >>