Legendre polynomial (chart) Calculator

Calculates a table of the Legendre polynomial Pn(x) and draws the chart.

 n n=0,1,2,... [ initial value x -1≦x≦1 increment repetition ]
 $\normal Legendre\ polinomial\ P_n(x)\\[10](1)\ (1-x^2)y''-2xy'+n(n+1)y=0\\\hspace{25}y=P_n(x)\\[10](2)\ {\large\frac{1}{sqrt{1-2xt+t^2}}}={\large\sum_{n=0}^{\infty}} P_n(x)t^n\\(3)\hspace{5}{\large\int_{\tiny -1}^{\hspace{25}\tiny 1}}P_n(x)P_m(x)dx={\large\frac {2}{2n+1}}\delta_{mn}\\(4)\ P_n(x)={}_{\small 2}F_{\small 1} (-n,n+1;\ 1;\frac{1-x}{2})\\$

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