Legendre Polynomials (Graph)
Calculates and graphs a table of the Legendre polynomial Pn(x).
| \(\normalsize Legendre\ polynomial\ P_n(x)\\ (1)\ (1-x^2)y''-2xy'+n(n+1)y=0\\ \hspace{25px}y=P_n(x)\\ (2)\ {\large\frac{1}{\sqrt{1-2xt+t^2}}}={\large\displaystyle \sum_{n=0}^{\infty}} P_n(x)t^n\\ (3)\hspace{5px}{\large\int_{\tiny -1}^{\tiny 1}}P_n(x)P_m(x)dx={\large\frac {2}{2n+1}}\delta_{mn}\\ (4)\ P_n(x)={}_{\small 2}F_{\small 1} (-n,n+1;\ 1;\frac{1-x}{2})\\\) |
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