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

Legendre polynomial (chart)
 [1-2] /2 Disp-Num5103050100200
[1]  2019/02/26 19:38   Male / Under 20 years old / High-school/ University/ Grad student / Very /
Purpose of use
Using
Comment/Request
good
[2]  2015/05/18 05:15   Male / 60 years old level or over / A teacher / A researcher / Very /
Purpose of use
Wrote my own program and need to compare values.
Comment/Request
A really great tool/website. Thank you.

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