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Nodes and weights for the Gauss-Lobatto integration method

TOP/Numerical integration/Gauss-Robert Numerical Integration
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Calculate the nodes and weights for the Gauss-Lobatto numerical integration.
\(\normalsize Gauss-Lobatto\ quadrature\\ {\large\int_{\small -1}^{\small 1}}f(x)dx\simeq{\large\frac{2}{n(n-1)}}(f(-1)+f(1))+{\large\displaystyle \sum_{\small i=2}^{n-1}}w_{i}f(x_i)\\\ nodes\hspace{30px} x_i:\ the\ i-th\ zeros\ of\ P_{n-1}^{'}(x)\\\ weights\hspace{15px} w_i={\large\frac{2}{n(n-1)[P_{n-1}(x_i)]^2}}\\\)
n
n=2,3,4,..,100
\(\normalsize Gaussian\ quadrature\\ \hspace{20px} {\large\int_{\small a}^{\small b}}w(x)f(x)dx\simeq{\large\displaystyle \sum_{\small i=1}^{n}}w_{i}f(x_i)\\ Gauss-Lobatto\ quadrature\\ \hspace{30px} interval(a,b):\hspace{20px} [-1,\ 1]\\ \hspace{30px} w(x):\hspace{80px} 1\\ \hspace{30px} polynomials:\hspace{10px} P{'}_{n-1} (x)\\ \)

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