L n(x)=(e^x/n!)d^n/dx^n(x^n e^(-x))

Theorem

The following formula holds: $$L_n(x) = \dfrac{e^x}{n!} \dfrac{\mathrm{d}^n}{\mathrm{d}x^n} (x^n e^{-x}),$$ where $L_n$ denotes Laguerre L and $e^x$ denotes the exponential function.

References

• 1968: W.W. Bell: Special Functions for Scientists and Engineers ... (previous) ... (next): Theorem 6.2