# KEX-Rrlϕ

## L(a,b)̐ϕKEX-Rrϖ@ŌvZ܂B

 $\normal Gauss-Jacobi\ quadrature\\ {\large\int_{\small -1}^{\hspace{25}\small 1}}(1-x)^{\alpha}(1+x)^{\beta}f(x)dx\simeq{\large\sum_{\small i=1}^{n}}w_{i}f(x_i)\\ {\large\int_{\small -1}^{\hspace{25}\small 1}}g(x)dx\simeq{\large\sum_{\small i=1}^{n}}{\large\frac{w_i}{(1-x_i)^{\alpha}(1+x_i)^{\beta}}}g(x_i)\\\hspace{130}g(x)=(1-x)^{\alpha}(1+x)^{\beta}f(x)\\$
 g(x) f(x) ϐ , (a , b ) 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 n=2,3,4,..,100
 61014182226303438424650
 ϕ֐f(x)́A͓Ił邱ƂƎ֐łȂƂOƂĂ܂B$\normal Gaussian\ quadrature\\\hspace{20} {\large\int_{\small a}^{\hspace{25}\small b}}w(x)f(x)dx\simeq{\large\sum_{\small i=1}^{n}}w_{i}f(x_i), \hspace{20} {\large\int_{\small a}^{\hspace{25}\small b}}g(x)dx\simeq{\large\sum_{\small i=1}^{n}}{\large\frac{w_{i}}{w(x_i)}}g(x_i)\\Gauss-Jacobi\ quadrature\\\hspace{30} interval(a,b):\hspace{20} (-1,\ 1)\\\hspace{30} w(x):\hspace{80} (1-x)^{\alpha}(1+x)^{\beta}\\\hspace{30} polynomialsl:\hspace{10} J_n^{\alpha,\beta} (x)\\$

AP[gɂ͒L܂B
M܂B

y KEX-Rrlϕ z̃AP[gL
j
N
20Ζ 20Α 30Α 40Α 50Α 60Έȏ
E
Ew ZEEwEw@ w ЈE c GWjA tE ̑
̌vZ
ɖɗ ɗ ɗ ɗȂ
gpړI
ӌEzioO񍐂) oOɊւ (AP[gj
vZoO(͒lƊԈĂ錋ʁAʁAQlȂ)
oO(ԈĂƐȂ)
AP[g͉Lɂql̐ƂČfڂĂƂ܂B