第１種チェビシェフ多項式（グラフ）

\(\normalsize Chebyshev\ polynomial\\ \hspace{120px} of\ the\ 1st\ kind\ T_n(x)\\ (1)\ (1-x^2)y''-xy'+n^2y=0\\ \hspace{25px} y=T_n(x)\\ (2)\ {\large\frac{1-xt}{1-2xt+t^2}}={\large\displaystyle \sum_{n=0}^{\infty}} T_n(x)t^n\\ (3) {\large\int_{\tiny -1}^{\tiny 1}\frac{T_n(x)T_m(x)}{\sqrt{1-x^2}}}dx={\large\left\{{ {\large\frac{\pi}{2}}\delta_{mn}\ for\ m,n\ne 0\atop \pi\hspace{20px}for\ m=n=0}\right.}\\ (4)\ T_n(x)={}_{\small 2}F_{\small 1} (-n,n;\ \frac{1}{2};\frac{1-x}{2})\\ \hspace{65px}= \cos(n\cdot \cos^{-1}x)\\\)