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Nodes and weights for the second-kind Gauss–Chebyshev integration method

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Calculates the nodes and weights for the second-kind Gauss–Chebyshev numerical integration.
\(\normalsize (1)\ {\large\int_{\small -1}^{\small 1}}\sqrt{1-x^2}f(x)dx\simeq {\large\displaystyle \sum_{\small i=1}^{n}}w_{i}f(x_i)\\ (2)\ f(x)\rightarrow {\large \frac{g(x)}{\sqrt{1-x^2}}}\\ \hspace{20px}{\large\int_{\small -1}^{\small 1}}g(x)dx\simeq {\large\displaystyle \sum_{\small i=1}^{n}}{\large \frac{w_i}{\sqrt{1-x_i^2}}}g(x_i)\\ \hspace{5px}nodes\hspace{35px} x_i=- \cos{\frac{(2i-1)\pi}{2n}}\\ \hspace{5px}weights\hspace{20px} w_i={\large\frac{\pi}{n}}\\ \)
order n
n=2,3,4,..,100
\(\normalsize Gaussian\ quadrature\\ \hspace{10px} {\large\int_{\small a}^{\small b}}w(x)f(x)dx\simeq{\large\displaystyle \sum_{\small i=1}^{n}}w_{i}f(x_i), \ {\large\int_{\small a}^{\small b}}g(x)dx\simeq{\large\displaystyle \sum_{\small i=1}^{n}}{\large\frac{w_{i}}{w(x_i)}}g(x_i)\\Gauss-Chebyshev\ 2nd\ quadrature\\ \hspace{30px} interval(a,b):\hspace{20px} [-1,\ 1]\\ \hspace{30px} w(x):\hspace{80px} \sqrt{1-x^2}\\ \hspace{30px} polynomialsl:\hspace{10px} U_n (x)\\ \)

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