## Calculates the integral of the given function f(x) over the interval (a,b) using Gaussian quadrature. (i.e. Gauss-Legendre, Gauss-Chebyshev 1st, Gauss-Chebyshev 2nd, Gauss-Laguerre, Gauss-Hermite, Gauss-Jacobi, Gauss-Lobatto and Gauss-Kronrod)

kinds
 Legendre Chebyshev 1st Chebyshev 2nd Laguerre Hermite Jacobi Lobatto Kronrod f(x)
order n
 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100
a
 , b
α
 β
 6dgt10dgt14dgt18dgt22dgt26dgt30dgt34dgt38dgt42dgt46dgt50dgt
 $\normal Gaussian\ quadrature\\\hspace{30} {\large\int_{\small a}^{\hspace{25}\small b}}w(x)f(x)dx\simeq{\large\sum_{\small i=1}^{n}}w_{i}f(x_i)\\\vspace{10}\hspace{20} Quadrature \hspace{30} interval \hspace{10} w(x) \hspace{30} polynomials\\\vspace{5}(1)\ Legendre \hspace{50} [-1,\ 1] \hspace{25} 1 \hspace{90} P_n(x)\\(2)\ Chebyshev\ 1st \hspace{5} (-1,\ 1) \hspace{10} {\large\frac{1}{\sqrt{1-x^2}}} \hspace{70} T_n(x) \\(3)\ Chebyshev\ 2nd \hspace{5} [-1,\ 1] \hspace{10} \sqrt{1-x^2} \hspace{65} U_n(x) \\(4)\ Laguerre \hspace{50} [0,\infty) \hspace{20} x^{\alpha} e^{-x} \hspace{65} L_n^\alpha (x) \\(5)\ Hermite \hspace{50} (-\infty,\infty) \hspace{10} e^{-x^2} \hspace{70} H_n (x) \\(6)\ Jacobi \hspace{75} (-1,\ 1) \hspace{10} (1-x)^{\alpha}(1+x)^{\beta} \hspace{5} J_n^{\alpha,\beta} (x) \\(7)\ Lobatto \hspace{60} [-1,\ 1] \hspace{25} 1 \hspace{80} P_{n-1}^' (x)\\(8)\ Kronrod \hspace{50} [-1,\ 1] \hspace{25} 1 \hspace{90} P_n(x)\\$

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