# KEX-G~[glϕ

## (-,)̐ϕKEX-G~[gϖ@ŌvZ܂B

 $\normal Gauss-Hermite\ quadrature\\[10] {\large\int_{\small -\infty}^{\hspace{25}\small \infty}}e^{-x^2}f(x)dx\simeq{\large\sum_{\small i=1}^{n}}w_{i}f(x_i)\\ {\large\int_{\small -\infty}^{\hspace{25}\small \infty}}g(x)dx\simeq{\large\sum_{\small i=1}^{n}}w_{i}e^{x_i^2}g(x_i)\\\vspace{20}$
 g(x) f(x) 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
 61014182226303438424650
 ϕ֐f(x)́A͓Ił邱ƂƎ֐łȂƂOƂĂ܂B$\normal Gaussian\ quadrature\\\hspace{10} {\large\int_{\small a}^{\hspace{25}\small b}}w(x)f(x)dx\simeq{\large\sum_{\small i=1}^{n}}w_{i}f(x_i), \ {\large\int_{\small a}^{\hspace{25}\small b}}g(x)dx\simeq{\large\sum_{\small i=1}^{n}}{\large\frac{w_{i}}{w(x_i)}}g(x_i)\\Gauss-Hermite\ quadrature\\\hspace{30} interval(a,b):\hspace{20} (-\infty,\infty)\\\hspace{30} w(x):\hspace{80} e^{-x^2}\\\hspace{30} polynomialsl:\hspace{10} H_n (x) \\$

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