# KEXϖ@()

## ϕԁia,bj̐ϕlXȃKEXϖ@ŌvZ܂B (KEX]WhϕA1FrVFtϕA2FrVFtϕAQ[ϕAG~[gϕARrϕAo[gϕANbhϕ)

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 Legendre Chebyshev 1st Chebyshev 2nd Laguerre Hermite Jacobi Lobatto Kronrod f(x)
n
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 61014182226303438424650
 $\normal Gaussian\ quadrature\\\hspace{30} {\large\int_{\small a}^{\hspace{25}\small b}}w(x)f(x)dx\simeq{\large\sum_{\small i=1}^{n}}w_{i}f(x_i)\\\vspace{10}\hspace{20} Quadrature \hspace{30} interval \hspace{10} w(x) \hspace{30} polynomials\\\vspace{5}(1)\ Legendre \hspace{50} [-1,\ 1] \hspace{25} 1 \hspace{90} P_n(x)\\(2)\ Chebyshev\ 1st \hspace{5} (-1,\ 1) \hspace{10} {\large\frac{1}{\sqrt{1-x^2}}} \hspace{70} T_n(x) \\(3)\ Chebyshev\ 2nd \hspace{5} [-1,\ 1] \hspace{10} \sqrt{1-x^2} \hspace{65} U_n(x) \\(4)\ Laguerre \hspace{50} [0,\infty) \hspace{20} x^{\alpha} e^{-x} \hspace{65} L_n^\alpha (x) \\(5)\ Hermite \hspace{50} (-\infty,\infty) \hspace{10} e^{-x^2} \hspace{70} H_n (x) \\(6)\ Jacobi \hspace{75} (-1,\ 1) \hspace{10} (1-x)^{\alpha}(1+x)^{\beta} \hspace{5} J_n^{\alpha,\beta} (x) \\(7)\ Lobatto \hspace{60} [-1,\ 1] \hspace{25} 1 \hspace{80} P_{n-1}^' (x)\\(8)\ Kronrod \hspace{50} [-1,\ 1] \hspace{25} 1 \hspace{90} P_n(x)\\$

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