Laguerre Polynomials (Graph)
Calculate the table for the Laguerre polynomial Ln(x) and plot it.
| \(\normalsize Laguerre\ polynomial\ L_n(x)\\ (1)\ xy''+(1-x)y'+ny=0\\ \hspace{25px} y=L_n(x)\\ (2)\ {\large\frac{\large e^{-\frac{xt}{1-t}}}{1-t}}={\large\displaystyle \sum_{n=0}^{\infty}}L_n(x)t^n\\ \hspace{20px}{\large\int_{\tiny 0}^{\tiny \infty}}L_n(x)L_m(x)e^{-x}dx=\delta_{mn}\\ (3)\ L_n(x)={}_{\small 1}F_{\small 1} (-n;\ 1;x)\\\) |
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