{"id":6611,"date":"2023-06-29T11:57:18","date_gmt":"2023-06-29T02:57:18","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=6611"},"modified":"2023-07-05T09:55:00","modified_gmt":"2023-07-05T00:55:00","slug":"maxima-%e3%81%a7%e3%83%95%e3%83%bc%e3%83%aa%e3%82%a8%e7%b4%9a%e6%95%b0%e5%b1%95%e9%96%8b%e3%81%ae%e5%95%8f%e9%a1%8c","status":"publish","type":"page","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e7%90%86%e5%b7%a5%e7%b3%bb%e3%81%ae%e6%95%b0%e5%ad%a6c\/maxima-%e3%81%a7%e7%90%86%e5%b7%a5%e7%b3%bb%e3%81%ae%e6%95%b0%e5%ad%a6c\/maxima-%e3%81%a6%e3%82%99%e3%83%95%e3%83%bc%e3%83%aa%e3%82%a8%e8%a7%a3%e6%9e%90\/maxima-%e3%81%a7%e3%83%95%e3%83%bc%e3%83%aa%e3%82%a8%e7%b4%9a%e6%95%b0%e5%b1%95%e9%96%8b%e3%81%ae%e5%95%8f%e9%a1%8c\/","title":{"rendered":"Maxima \u3067\u30d5\u30fc\u30ea\u30a8\u7d1a\u6570\u5c55\u958b\u306e\u4f8b\u984c\u3092\u89e3\u304f"},"content":{"rendered":"

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\u30d5\u30fc\u30ea\u30a8\u7d1a\u6570\u5c55\u958b\u306e\u4f8b\u984c<\/h3>\n

\u533a\u9593 $[-1: 1]$ \u3067\u5b9a\u7fa9\u3055\u308c\u305f\u95a2\u6570 $f(x) = 1 – |x|$ \u304c\u533a\u9593\u5916\u3067\u306f\u5468\u671f $2$ \u306e\u5468\u671f\u95a2\u6570\u3060\u3068\u3057\u3066\uff0c\u305d\u306e\u30d5\u30fc\u30ea\u30a8\u7d1a\u6570\u5c55\u958b\u3092\u6c42\u3081\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n

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\/* -L <= x <= L \u3067\u5b9a\u7fa9\u3055\u308c\u305f\u95a2\u6570 f0(x) *\/<\/span>\r\nf0<\/span>(<\/span>x<\/span>)<\/span>:=<\/span> 1<\/span> -<\/span> abs<\/span>(<\/span>x<\/span>)<\/span>;\r\n\r\n\/* f0(x) \u3092\u4efb\u610f\u5468\u671f 2L \u306e\u5468\u671f\u95a2\u6570\u306b\u3059\u308b\u5c0f\u9053\u5177 *\/<\/span>\r\nxcyc<\/span>(<\/span>x<\/span>, L<\/span>)<\/span>:=<\/span> x<\/span> -<\/span> 2*<\/span>L<\/span>*<\/span>floor<\/span>((<\/span>x<\/span>+<\/span>L<\/span>)<\/span>\/<\/span>(<\/span>2*<\/span>L<\/span>))<\/span>;\r\n\r\n\/* L = 1 *\/<\/span>\r\nf<\/span>(<\/span>x<\/span>)<\/span>:=<\/span> f0<\/span>(<\/span>xcyc<\/span>(<\/span>x<\/span>, 1<\/span>))<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[1]:<\/div>\n
\\[\\tag{${\\it \\%o}_{1}$}f_{0}\\left(x\\right):=1-\\left| x\\right| \\]<\/div>\n<\/div>\n
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\\[\\tag{${\\it \\%o}_{2}$}{\\it xcyc}\\left(x , L\\right):=x-2\\,L\\,\\left \\lfloor \\frac{x+L}{2\\,L} \\right \\rfloor\\]<\/div>\n<\/div>\n
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\\[\\tag{${\\it \\%o}_{3}$}f\\left(x\\right):=f_{0}\\left({\\it xcyc}\\left(x , 1\\right)\\right)\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u533a\u9593 $-1 \\le x \\le 1$ \u3067\u5b9a\u7fa9\u3055\u308c\u305f\u95a2\u6570 $f_0(x)$ \u3068\uff0c\u5468\u671f $2$ \u306e\u5468\u671f\u95a2\u6570 $f(x)$ \u3092\u305d\u308c\u305e\u308c\u30b0\u30e9\u30d5\u306b\u3057\u3066\u307f\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[2]:<\/div>\n
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plot2d<\/span>(<\/span>f0<\/span>(<\/span>x<\/span>)<\/span>, [<\/span>x<\/span>, -<\/span>1<\/span>, 1]<\/span>, [<\/span>x<\/span>, -<\/span>5<\/span>, 5]<\/span>, [<\/span>xtics<\/span>, 1]<\/span>, [<\/span>ylabel<\/span>,\"f0(x)\"<\/span>])<\/span>$\r\nplot2d<\/span>(<\/span>f<\/span>(<\/span>x<\/span>)<\/span>, [<\/span>x<\/span>, -<\/span>5<\/span>, 5]<\/span>, [<\/span>xtics<\/span>, 1]<\/span>, [<\/span>ylabel<\/span>,\"f(x)\"<\/span>])<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u5b9a\u7fa9\u3069\u304a\u308a\u306b\u30d5\u30fc\u30ea\u30a8\u7d1a\u6570\u5c55\u958b\u3092\u5b9a\u7fa9\u3059\u308b\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308b\u304c…<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[3]:<\/div>\n
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declare<\/span>(<\/span>n<\/span>, integer<\/span>)<\/span>$\r\n\r\na<\/span>(<\/span>n<\/span>,L<\/span>)<\/span>:=<\/span> 1\/<\/span>L<\/span> *<\/span> integrate<\/span>(<\/span>f0<\/span>(<\/span>x<\/span>)<\/span>*<\/span>cos<\/span>(<\/span>n<\/span>*<\/span>%pi<\/span>*<\/span>x<\/span>\/<\/span>L<\/span>)<\/span>, x<\/span>, -<\/span>L<\/span>, L<\/span>)<\/span>;\r\nb<\/span>(<\/span>n<\/span>,L<\/span>)<\/span>:=<\/span> 1\/<\/span>L<\/span> *<\/span> integrate<\/span>(<\/span>f0<\/span>(<\/span>x<\/span>)<\/span>*<\/span>sin<\/span>(<\/span>n<\/span>*<\/span>%pi<\/span>*<\/span>x<\/span>\/<\/span>L<\/span>)<\/span>, x<\/span>, -<\/span>L<\/span>, L<\/span>)<\/span>;\r\n\r\nFourier<\/span>(<\/span>n<\/span>,x<\/span>,L<\/span>)<\/span>:=<\/span> a<\/span>(<\/span>0<\/span>)<\/span>\/<\/span>2<\/span> +<\/span> sum<\/span>(<\/span>a<\/span>(<\/span>i<\/span>,L<\/span>)<\/span>*<\/span>cos<\/span>(<\/span>i<\/span>*<\/span>%pi<\/span>*<\/span>x<\/span>\/<\/span>L<\/span>)<\/span> +<\/span> \r\n                              b<\/span>(<\/span>i<\/span>,L<\/span>)<\/span>*<\/span>sin<\/span>(<\/span>i<\/span>*<\/span>%pi<\/span>*<\/span>x<\/span>\/<\/span>L<\/span>)<\/span>, i<\/span>, 1<\/span>, n<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[3]:<\/div>\n
\\[\\tag{${\\it \\%o}_{9}$}a\\left(n , L\\right):=\\frac{1}{L}\\,{\\it integrate}\\left(f_{0}\\left(x\\right)\\,\\cos \\left(\\frac{n\\,\\pi\\,x}{L}\\right) , x , -L , L\\right)\\]<\/div>\n<\/div>\n
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\\[\\tag{${\\it \\%o}_{10}$}b\\left(n , L\\right):=\\frac{1}{L}\\,{\\it integrate}\\left(f_{0}\\left(x\\right)\\,\\sin \\left(\\frac{n\\,\\pi\\,x}{L}\\right) , x , -L , L\\right)\\]<\/div>\n<\/div>\n
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\\[\\tag{${\\it \\%o}_{11}$}{\\it Fourier}\\left(n , x , L\\right):=\\frac{a\\left(0\\right)}{2}+{\\it sum}\\left(a\\left(i , L\\right)\\,\\cos \\left(\\frac{i\\,\\pi\\,x}{L}\\right)+b\\left(i , L\\right)\\,\\sin \\left(\\frac{i\\,\\pi\\,x}{L}\\right) , i , 1 , n\\right)\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u3060\u3068\u3048\u3070 $a_1 = $ a(1,1)<\/code> \u306e\u8a08\u7b97\u3092\u307f\u308c\u3070\u308f\u304b\u308b\u3088\u3046\u306b\uff0c\u7d76\u5bfe\u5024\u3092\u542b\u3080\u7a4d\u5206\u306f\u305d\u306e\u307e\u307e\u3067\u306f\u3060\u3081\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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a<\/span>(<\/span>1<\/span>,1<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[4]:<\/div>\n
\\[\\tag{${\\it \\%o}_{12}$}\\int_{-1}^{1}{\\left(1-\\left| x\\right| \\right)\\,\\cos \\left(\\pi\\,x\\right)\\;dx}\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u4eba\u306e\u624b\u3067\u7a4d\u5206\u3059\u308b\u3068\u304d\u3068\u540c\u69d8\u306b\uff0c\u5834\u5408\u5206\u3051\u3067\u7d76\u5bfe\u5024\u3092\u306f\u305a\u3059\uff0c\u3064\u307e\u308a $x < 0$ \u306a\u3089 $f_0(x) = 1 – |x| = 1 + x $\uff0c$x > 0 $ \u306a\u3089 $f0(x) = 1 – |x| = 1 – x$ \u306e\u3088\u3046\u306b\u3059\u308b\u3002<\/p>\n
\u3064\u307e\u308a\uff0c$L = 1$ \u3068\u3057\u3066\uff0c\u7a4d\u5206\u533a\u9593\u3092\u5206\u3051\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u3059\u308b\u3002\u7a4d\u5206\u533a\u9593\u3092\u6b63\u306e\u533a\u9593\u3068\u8ca0\u306e\u533a\u9593\u306b\u5206\u3051\u308b\u3053\u3068\u306b\u3088\u3063\u3066\uff0c\u7d76\u5bfe\u5024\u3092\u542b\u3080\u95a2\u6570 $f_0(x)$ \u3067\u3082\u3061\u3083\u3093\u3068\u7a4d\u5206\u3057\u3066\u304f\u308c\u308b\u3088\u3046\u3060\u3002<\/p>\n
$$\\int_{-1}^1 f_0(x) \\cos\\left(n\\pi x\\right)\\,dx = \\int_{-1}^0 f_0(x) \\cos\\left(n\\pi x\\right)\\,dx + \\int_{0}^1 f_0(x) \\cos\\left(n\\pi x\\right)\\,dx$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[5]:<\/div>\n
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a<\/span>(<\/span>n<\/span>,L<\/span>)<\/span>:=<\/span> 1\/<\/span>L<\/span> *<\/span> (<\/span>integrate<\/span>(<\/span>f0<\/span>(<\/span>x<\/span>)<\/span>*<\/span>cos<\/span>(<\/span>n<\/span>*<\/span>%pi<\/span>*<\/span>x<\/span>\/<\/span>L<\/span>)<\/span>, x<\/span>, -<\/span>L<\/span>, 0<\/span>)<\/span> +<\/span> \r\n                integrate<\/span>(<\/span>f0<\/span>(<\/span>x<\/span>)<\/span>*<\/span>cos<\/span>(<\/span>n<\/span>*<\/span>%pi<\/span>*<\/span>x<\/span>\/<\/span>L<\/span>)<\/span>, x<\/span>, 0<\/span>, L<\/span>))<\/span>$\r\nb<\/span>(<\/span>n<\/span>,L<\/span>)<\/span>:=<\/span> 1\/<\/span>L<\/span> *<\/span> (<\/span>integrate<\/span>(<\/span>f0<\/span>(<\/span>x<\/span>)<\/span>*<\/span>sin<\/span>(<\/span>n<\/span>*<\/span>%pi<\/span>*<\/span>x<\/span>\/<\/span>L<\/span>)<\/span>, x<\/span>, -<\/span>L<\/span>, 0<\/span>)<\/span> +<\/span> \r\n                integrate<\/span>(<\/span>f0<\/span>(<\/span>x<\/span>)<\/span>*<\/span>sin<\/span>(<\/span>n<\/span>*<\/span>%pi<\/span>*<\/span>x<\/span>\/<\/span>L<\/span>)<\/span>, x<\/span>, 0<\/span>, L<\/span>))<\/span>$\r\n\r\nFourier<\/span>(<\/span>n<\/span>,x<\/span>,L<\/span>)<\/span>:=<\/span> a<\/span>(<\/span>0<\/span>,L<\/span>)<\/span>\/<\/span>2<\/span> +<\/span> sum<\/span>(<\/span>a<\/span>(<\/span>i<\/span>,L<\/span>)<\/span>*<\/span>cos<\/span>(<\/span>i<\/span>*<\/span>%pi<\/span>*<\/span>x<\/span>\/<\/span>L<\/span>)<\/span> +<\/span> \r\n                                b<\/span>(<\/span>i<\/span>,L<\/span>)<\/span>*<\/span>sin<\/span>(<\/span>i<\/span>*<\/span>%pi<\/span>*<\/span>x<\/span>\/<\/span>L<\/span>)<\/span>, i<\/span>, 1<\/span>, n<\/span>)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u30d5\u30fc\u30ea\u30a8\u4fc2\u6570 $a_n, b_n$ \u306f…<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[6]:<\/div>\n
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a<\/span>(<\/span>n<\/span>,1<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[6]:<\/div>\n
\\[\\tag{${\\it \\%o}_{18}$}\\frac{2}{\\pi^2\\,n^2}-\\frac{2\\,\\left(-1\\right)^{n}}{\\pi^2\\,n^2}\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[7]:<\/div>\n
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b<\/span>(<\/span>n<\/span>,1<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[7]:<\/div>\n
\\[\\tag{${\\it \\%o}_{19}$}0\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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$a_n$ \u306f $n$ \u306e\u5076\u5947\u306b\u3088\u3063\u3066\u30bc\u30ed\u306b\u306a\u308b\u5834\u5408\u304c\u3042\u308b\u306e\u3067\uff0c$n=10$ \u307e\u3067\u8868\u793a\u3057\u3066\u307f\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[8]:<\/div>\n
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for<\/span> i<\/span>:<\/span>0<\/span> thru<\/span> 10<\/span> do<\/span>(<\/span>print<\/span>(<\/span>\"a(\"<\/span>,i<\/span>,\")=\"<\/span>, a<\/span>(<\/span>i<\/span>,1<\/span>)))<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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a( \\(0\\) )= \\(1\\)<\/div>\n<\/div>\n
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a( \\(1\\) )= \\(\\frac{4}{\\pi^2}\\)<\/div>\n<\/div>\n
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a( \\(2\\) )= \\(0\\)<\/div>\n<\/div>\n
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a( \\(3\\) )= \\(\\frac{4}{9\\,\\pi^2}\\)<\/div>\n<\/div>\n
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a( \\(4\\) )= \\(0\\)<\/div>\n<\/div>\n
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a( \\(5\\) )= \\(\\frac{4}{25\\,\\pi^2}\\)<\/div>\n<\/div>\n
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a( \\(6\\) )= \\(0\\)<\/div>\n<\/div>\n
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a( \\(7\\) )= \\(\\frac{4}{49\\,\\pi^2}\\)<\/div>\n<\/div>\n
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a( \\(8\\) )= \\(0\\)<\/div>\n<\/div>\n
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a( \\(9\\) )= \\(\\frac{4}{81\\,\\pi^2}\\)<\/div>\n<\/div>\n
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a( \\(10\\) )= \\(0\\)<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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$n = 3, 5, 7$ \u306e\u30d5\u30fc\u30ea\u30a8\u7d1a\u6570\u3092\u6c42\u3081\uff0c\u30b0\u30e9\u30d5\u306b\u3057\u3066\u307f\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[9]:<\/div>\n
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f3<\/span>:<\/span> Fourier<\/span>(<\/span>3<\/span>,x<\/span>,1<\/span>)<\/span>;\r\nf5<\/span>:<\/span> Fourier<\/span>(<\/span>5<\/span>,x<\/span>,1<\/span>)<\/span>;\r\nf7<\/span>:<\/span> Fourier<\/span>(<\/span>7<\/span>,x<\/span>,1<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[9]:<\/div>\n
\\[\\tag{${\\it \\%o}_{21}$}\\frac{4\\,\\cos \\left(3\\,\\pi\\,x\\right)}{9\\,\\pi^2}+\\frac{4\\,\\cos \\left(\\pi\\,x\\right)}{\\pi^2}+\\frac{1}{2}\\]<\/div>\n<\/div>\n
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\\[\\tag{${\\it \\%o}_{22}$}\\frac{4\\,\\cos \\left(5\\,\\pi\\,x\\right)}{25\\,\\pi^2}+\\frac{4\\,\\cos \\left(3\\,\\pi\\,x\\right)}{9\\,\\pi^2}+\\frac{4\\,\\cos \\left(\\pi\\,x\\right)}{\\pi^2}+\\frac{1}{2}\\]<\/div>\n<\/div>\n
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\\[\\tag{${\\it \\%o}_{23}$}\\frac{4\\,\\cos \\left(7\\,\\pi\\,x\\right)}{49\\,\\pi^2}+\\frac{4\\,\\cos \\left(5\\,\\pi\\,x\\right)}{25\\,\\pi^2}+\\frac{4\\,\\cos \\left(3\\,\\pi\\,x\\right)}{9\\,\\pi^2}+\\frac{4\\,\\cos \\left(\\pi\\,x\\right)}{\\pi^2}+\\frac{1}{2}\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[10]:<\/div>\n
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plot2d<\/span>([<\/span>f<\/span>(<\/span>x<\/span>)<\/span>, f7<\/span>, f5<\/span>, f3<\/span>]<\/span>, [<\/span>x<\/span>, -<\/span>3<\/span>, 4]<\/span>, \r\n       [<\/span>legend<\/span>, \"f(x)\"<\/span>, \"n=7\"<\/span>, \"n=5\"<\/span>, \"n=3\"<\/span>])<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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$n=15$ \u304f\u3089\u3044\u3060\u3068\uff0c\u304b\u306a\u308a $f(x)$ \u306b\u8fd1\u3044\u611f\u3058\u304c\u3042\u3089\u308f\u308c\u3066\u3044\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[11]:<\/div>\n
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plot2d<\/span>([<\/span>f<\/span>(<\/span>x<\/span>)<\/span>, Fourier<\/span>(<\/span>15<\/span>,x<\/span>,1<\/span>)]<\/span>, [<\/span>x<\/span>, -<\/span>3<\/span>, 4]<\/span>, \r\n       [<\/span>legend<\/span>, \"f(x)\"<\/span>, \"n=15\"<\/span>])<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u53c2\u8003\uff1afourie \u30d1\u30c3\u30b1\u30fc\u30b8\u3092\u4f7f\u3046\u5834\u5408<\/h3>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[12]:<\/div>\n
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load<\/span>(<\/span>\"fourie\"<\/span>)<\/span>$ \/* \u30d1\u30c3\u30b1\u30fc\u30b8\u540d\u6ce8\u610f\uff01 fourier \u3067\u306f\u306a\u3044\u3002*\/<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[13]:<\/div>\n
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f0<\/span>(<\/span>x<\/span>)<\/span>:=<\/span> 1<\/span> -<\/span> abs<\/span>(<\/span>x<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[13]:<\/div>\n
\\[\\tag{${\\it \\%o}_{29}$}f_{0}\\left(x\\right):=1-\\left| x\\right| \\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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<\/div>\n
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\u3084\u3063\u3066\u307f\u308c\u3070\u308f\u304b\u308b\u304c\uff0c\u7d76\u5bfe\u5024\u306e\u5834\u5408\u5206\u3051\u3092\u3057\u306a\u304f\u3066\u3082\uff0c\u3053\u306e\u30d1\u30c3\u30b1\u30fc\u30b8\u306f\u512a\u79c0\u3067\uff0c\u304d\u3061\u3093\u3068\u30d5\u30fc\u30ea\u30a8\u4fc2\u6570\u3092\u6c42\u3081\u3066\u304f\u308c\u308b\u3088\u3046\u3060\u3002\u3042\u308a\u304c\u305f\u3044\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[14]:<\/div>\n
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declare<\/span>(<\/span>n<\/span>, integer<\/span>)<\/span>$\r\nans<\/span>:<\/span> fourier<\/span>(<\/span>f0<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>, 1<\/span>)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\\[\\tag{${\\it \\%t}_{31}$}a_{0}=\\frac{1}{2}\\]<\/div>\n<\/div>\n
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\\[\\tag{${\\it \\%t}_{32}$}a_{n}=2\\,\\left(\\frac{1}{\\pi^2\\,n^2}-\\frac{\\left(-1\\right)^{n}}{\\pi^2\\,n^2}\\right)\\]<\/div>\n<\/div>\n
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\\[\\tag{${\\it \\%t}_{33}$}b_{n}=0\\]<\/div>\n<\/div>\n
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<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":33,"featured_media":0,"parent":2378,"menu_order":10,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-6611","page","type-page","status-publish","hentry","nodate","item-wrap"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/6611","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/users\/33"}],"replies":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/comments?post=6611"}],"version-history":[{"count":5,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/6611\/revisions"}],"predecessor-version":[{"id":6620,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/6611\/revisions\/6620"}],"up":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/2378"}],"wp:attachment":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/media?parent=6611"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}