# Chebyshev polynomial of the 2nd kind (chart) Calculator

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

 n n=0,1,2,... [ initial value x -1≦x≦1 increment repetition ]
 $\normal Chebyshev\ polinomial\\\hspace{120} of\ the\ 2nd\ kind\ U_n(x)\\[10](1)\ (1-x^2)y''-xy'+n^2y=0\\\hspace{25} y=U_n(x)\\[10](2)\ {\large\frac {1}{1-2xt+t^2}}={\large\sum_{n=0}^{\infty}} U_n(x)t^n\\(3)\ {\large\int_{\tiny -1}^{\hspace{25}\tiny 1}\sqrt{1-x^2}}U_n(x)U_m(x)dx={\large\frac{\pi}{2}}\delta_{mn}\\(4)\ U_n(x)=(n+1){}_{\small 2}F_{\small 1} (-n,n+2;\ {\large\frac{3}{2}};{\large\frac{1-x}{2}})\\\hspace{70}={\large\frac{sin((n+1)cos^{-1}x)}{sin(cos^{-1}x)}}\\$

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