拉盖尔多项式

\begin{equation} L_{n+1}^\alpha (x) = [(2n + 1 + \alpha - x)L_n^\alpha (x) - (n + \alpha )L_{n - 1}^\alpha (x)]/(n + 1) \end{equation}

\begin{equation} L_0^\alpha (x) = 1 \qquad L_1^\alpha (x) = 1 + \alpha - x \end{equation}

\begin{equation} L_n^\alpha (x) = \frac{x^{-\alpha} \mathrm{e} ^x}{n!} \frac{\mathrm{d}^{n}}{\mathrm{d}{x}^{n}} ( \mathrm{e} ^{-x} x^{n+\alpha}) \end{equation}