# Chebyshev polynomial of the 1st kind (chart) Calculator

## Calculates a table of the Chebyshev polynomial of the first kind Tn(x) and draws the chart.

 n n=0,1,2,... [ initial value x -1≦x≦1 increment repetition ]
 $\normal Chebyshev\ polinomial\\\hspace{120} of\ the\ 1st\ kind\ T_n(x)\\[10](1)\ (1-x^2)y''-xy'+n^2y=0\\\hspace{25} y=T_n(x)\\[10](2)\ {\large\frac{1-xt}{1-2xt+t^2}}={\large\sum_{n=0}^{\infty}} T_n(x)t^n\\(3) {\large\int_{\tiny -1}^{\hspace{25}\tiny 1}\frac{T_n(x)T_m(x)}{\sqrt{1-x^2}}}dx={\large\left\{{ {\large\frac{\pi}{2}}\delta_{mn}\ for\ m,n\ne 0\atop \pi\hspace{20}for\ m=n=0}\right.}\\(4)\ T_n(x)={}_{\small 2}F_{\small 1} (-n,n;\ \frac{1}{2};\frac{1-x}{2})\\\hspace{65}=cos(n\cdot cos^{-1}x)\\$

Chebyshev polynomial of the 1st kind (chart)
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