{"id":2362,"date":"2022-02-26T10:42:58","date_gmt":"2022-02-26T01:42:58","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=2362"},"modified":"2025-07-29T11:14:50","modified_gmt":"2025-07-29T02:14:50","slug":"%e3%83%95%e3%83%bc%e3%83%aa%e3%82%a8%e7%b4%9a%e6%95%b0","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\/%e3%83%95%e3%83%bc%e3%83%aa%e3%82%a8%e8%a7%a3%e6%9e%90\/%e3%83%95%e3%83%bc%e3%83%aa%e3%82%a8%e7%b4%9a%e6%95%b0\/","title":{"rendered":"\u30d5\u30fc\u30ea\u30a8\u7d1a\u6570"},"content":{"rendered":"

\u533a\u9593 \\(-\\pi \\le x \\le \\pi\\) \u3067\u5b9a\u7fa9\u3055\u308c\u305f\u95a2\u6570 \\(f(x)\\) \u306f\uff0c\u305d\u308c\u304c\u3069\u3093\u306a\u95a2\u6570\u3067\u3042\u3063\u3066\u3082\uff08\u533a\u9593\u5916\u3067\u306f\uff0c\u5468\u671f \\( 2\\pi \\) \u306e\u5468\u671f\u95a2\u6570\u3068\u307f\u306a\u3057\u3066\uff09\uff0c\u4e09\u89d2\u95a2\u6570 \\( \\cos, \\ \\sin \\) \u306e\u91cd\u306d\u5408\u308f\u305b\u3067\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u308b\u3002
\n<\/p>\n

\n

\u30d5\u30fc\u30ea\u30a8\u4fc2\u6570\u3068\u30d5\u30fc\u30ea\u30a8\u7d1a\u6570\u5c55\u958b<\/h3>\n
    \n
  1. \u533a\u9593 \\(-\\pi \\le x \\le \\pi\\) \u3067\u5b9a\u7fa9\u3055\u308c\u305f\u95a2\u6570 \\(f(x)\\) \u306f\uff0c\u305d\u308c\u304c\u3069\u3093\u306a\u95a2\u6570\u3067\u3042\u3063\u3066\u3082…<\/li>\n
  2. \uff08\u533a\u9593\u5916\u3067\u306f\uff0c\u5468\u671f \\( 2\\pi \\) \u306e\u5468\u671f\u95a2\u6570\u3068\u307f\u306a\u3057\u3066\uff09<\/li>\n
  3. \u4e09\u89d2\u95a2\u6570 \\(\\cos, \\ \\sin\\) \u306e\u91cd\u306d\u5408\u308f\u305b\u3066\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u308b\uff01<\/li>\n<\/ol>\n

    \u3064\u307e\u308a\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u66f8\u3051\u308b\u3068\u3044\u3046\u3053\u3068\u3002
    \n$$ f(x) = \\frac{a_0}{2} + \\sum_{n=1}^{\\infty} \\bigl( a_n \\cos (n x) + b_n \\sin (n x) \\bigr) $$
    \n\u3053\u3053\u3067\uff0c\\(a_0, a_1, \\cdots, b_1, b_2, \\cdots\\) \u3092\u30d5\u30fc\u30ea\u30a8\u4fc2\u6570<\/b><\/span>\u3068\u547c\u3073\uff0c\u3053\u306e\u3088\u3046\u306a\u8868\u793a\u3092\u95a2\u6570 \\(f(x)\\) \u306e\u30d5\u30fc\u30ea\u30a8\u7d1a\u6570\u5c55\u958b<\/b><\/u><\/span>\u3068\u3044\u3046\u3002<\/p>\n

    \u3042\u308b\u95a2\u6570 \\(f(x)\\) \u306e\u30d5\u30fc\u30ea\u30a8\u7d1a\u6570\u5c55\u958b\u3092\u6c42\u3081\u3088\uff0c\u3068\u3044\u3046\u554f\u984c\u306f\uff0c\u3064\u307e\u308a\uff0c\\(f(x)\\) \u3092\u3046\u307e\u304f\u8868\u3059\u3088\u3046\u306b\u30d5\u30fc\u30ea\u30a8\u4fc2\u6570 \\(a_n, b_n\\) \u3092\u6c42\u3081\u3088\uff0c\u3068\u3044\u3046\u3053\u3068\u306b\u306a\u308b\u3002\u5148\u306b\u7b54\u3048\u3092\u66f8\u3044\u3066\u304a\u304f\u3068…<\/p>\n

    $$a_n = \\frac{1}{\\pi} \\int_{-\\pi}^{\\pi} f(x) \\cos (n x) \\, dx $$
    \n$$b_n = \\frac{1}{\\pi} \\int_{-\\pi}^{\\pi} f(x) \\sin (n x) \\, dx $$<\/p>\n

    \u4ee5\u4e0b\u306f\uff0c\u306a\u3093\u3067\u3053\u3046\u306a\u308b\u304b\u3068\u3044\u3046\u8a71\u3002\u307e\u305a\uff0c\u30d5\u30fc\u30ea\u30a8\u4fc2\u6570\u3092\u6c42\u3081\u308b\u3068\u304d\u306b\u4f7f\u3046\u306e\u304c\u300c\u4e09\u89d2\u95a2\u6570\u306e\u76f4\u4ea4\u6027<\/b><\/span>\u300d\u3068\u3044\u3046\u6027\u8cea\u3067\u3042\u308b\u3002<\/p>\n

    \u57fa\u672c\u30d9\u30af\u30c8\u30eb\u306e\u76f4\u4ea4\u6027\u3092\u4f8b\u3048\u8a71\u306b<\/h3>\n

    3\u6b21\u5143\u30d9\u30af\u30c8\u30eb\u306f\u4e00\u822c\u306b $$\\boldsymbol{a} = a_x \\boldsymbol{i} + a_y \\boldsymbol{j} + a_z \\boldsymbol{k}$$ \u306e\u3088\u3046\u306b\uff0c\u57fa\u672c\u30d9\u30af\u30c8\u30eb \\( \\boldsymbol{i}, \\boldsymbol{j}, \\boldsymbol{k}\\) \u3068\u6210\u5206 \\( a_x, a_y, a_z \\) \u3067\u66f8\u3051\u308b\u306e\u3067\u3042\u3063\u305f\u3002<\/p>\n

    \u3053\u306e\u57fa\u672c\u30d9\u30af\u30c8\u30eb\u306f\u5927\u304d\u3055\u304c \\(1\\) \u3067\u4e92\u3044\u306b\u76f4\u4ea4\u3057\u3066\u3044\u308b\u3002
    \n$$\\boldsymbol{e}_1 \\equiv \\boldsymbol{i}, \\quad \\boldsymbol{e}_2 \\equiv \\boldsymbol{j}, \\quad \\boldsymbol{e}_3 \\equiv \\boldsymbol{k}$$ \u3068\u66f8\u304f\u3068\uff0c\u3053\u306e\u6b63\u898f\u76f4\u4ea4\u6027\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u66f8\u3051\u308b\u3002
    \n$$ \\boldsymbol{e}_i \\cdot \\boldsymbol{e}_j = \\delta_{ij} =
    \n\\begin{cases}
    \n1 & (i = j) \\\\
    \n0\u00a0 & (i \\neq j)
    \n\\end{cases}
    \n$$ \u3053\u3053\u3067\uff0c\\(\\delta_{ij}\\) \u306f\u30af\u30ed\u30cd\u30c3\u30ab\u30fc\u306e\u30c7\u30eb\u30bf<\/b><\/span>\u3068\u547c\u3070\u308c\u308b\u8a18\u53f7\u3067\uff0c\\(i\\) \u3068 \\(j\\) \u304c\u7b49\u3057\u3044\u3068\u304d\u306b \\(1\\)\uff0c\u305d\u3046\u3067\u306a\u3044\u3068\u304d\u306f \\(0\\) \u3092\u4e0e\u3048\u308b\u3002\u3053\u306e\u3053\u3068\u306f\uff0c\u3064\u307e\u308a\u76f4\u4ea4\u3057\u3066\u3044\u308b\u3053\u3068\u3092\u8868\u3057\u3066\u3044\u308b\u3093\u3060\u3068\u7406\u89e3\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n

    \u3055\u3089\u306b\uff0c\u30d9\u30af\u30c8\u30eb\u306e\u6210\u5206\u3092 $$a_1 \\equiv a_x, \\quad a_2 \\equiv a_y, \\quad a_3 \\equiv a_z$$ \u306e\u3088\u3046\u306b\u66f8\u304d\u63db\u3048\u308b\u3068\uff0c
    \n$$ \\boldsymbol{a} = \\sum_{i=1}^{3} a_i \\boldsymbol{e}_i $$ \u3067\u3042\u308a\uff0c\u3053\u306e\u4e21\u8fba\u306b \\(\\boldsymbol{e}_j\\) \u3092\u5185\u7a4d\u3068\u3057\u3066\u304b\u3051\u3066\u3084\u308b\u3068\uff0c
    \n$$ \\boldsymbol{a} \\cdot\\boldsymbol{e}_j\u00a0 = \\sum_{i=1}^{3} a_i \\boldsymbol{e}_i\\cdot \\boldsymbol{e}_j = \\sum_{i=1}^{3} a_i \\delta_{ij} = a_j$$ \u3064\u307e\u308a\uff0c\u6210\u5206 \\(a_j\\) \u304c\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u5185\u7a4d\u306b\u3088\u3063\u3066\u6c42\u3081\u3089\u308c\u308b\u3002
    \n$$ a_j = \\boldsymbol{a} \\cdot\\boldsymbol{e}_j\u00a0 $$<\/p>\n

    \u88dc\u8db3\uff1a\u30af\u30ed\u30cd\u30c3\u30ab\u30fc\u306e\u30c7\u30eb\u30bf\u304c\u3089\u307f\u306e\u8a08\u7b97\u306b\u95a2\u3057\u3066<\/h4>\n

    \u5b66\u751f\u304b\u3089\u306e\u8cea\u554f\u304c\u3042\u3063\u305f\u306e\u3067\uff0c\u5ff5\u306e\u305f\u3081\u306b\u30af\u30ed\u30cd\u30c3\u30ab\u30fc\u306e\u30c7\u30eb\u30bf\u304c\u3089\u307f\u306e\u8a08\u7b97\u306b\u3064\u3044\u3066\u88dc\u8db3\u3057\u3066\u304a\u304f\u3002\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308b\u3053\u3068\u304c\u3059\u3050\u306b\u306f\u308f\u304b\u3089\u306a\u3044\u5834\u5408\uff1a<\/p>\n

    $$\\sum_{i=1}^{3} a_i \\,\\delta_{ij} = a_j$$<\/p>\n

    \u307e\u305a $\\color{red}{j=1}$ \u3068\u3057\u3066\u5de6\u8fba\u3092\u8a08\u7b97\u3057\u3066\u307f\u308b\u3068\uff0c<\/p>\n

    \\begin{eqnarray}
    \n\\sum_{i=1}^{3} a_i \\,\\delta_{i{\\color{red}{1}}} &=& a_1\\, \\delta_{1{\\color{red}{1}}} + a_2\\, \\delta_{2{\\color{red}{1}}}\u00a0 + a_3 \\, \\delta_{3{\\color{red}{1}}} \\\\
    \n&=& a_1\\cdot 1 + a_2\\cdot 0\u00a0 + a_3 \\cdot 0\\\\
    \n&=& a_{{\\color{red}{1}}}
    \n\\end{eqnarray}<\/p>\n

    $\\color{red}{j=2}$ \u306e\u5834\u5408\u306f\uff0c<\/p>\n

    \\begin{eqnarray}
    \n\\sum_{i=1}^{3} a_i \\,\\delta_{i{\\color{red}{2}}} &=& a_1\\, \\delta_{1{\\color{red}{2}}} + a_2\\, \\delta_{2{\\color{red}{2}}}\u00a0 + a_3 \\, \\delta_{3{\\color{red}{2}}} \\\\
    \n&=& a_1\\cdot 0 + a_2\\cdot 1\u00a0 + a_3 \\cdot 0\\\\
    \n&=& a_{\\color{red}{2}}
    \n\\end{eqnarray}<\/p>\n

    \u3068\u306a\u308b\u3057\uff0c$\\color{red}{j=3}$ \u306e\u5834\u5408\u306f\uff0c<\/p>\n

    \\begin{eqnarray}
    \n\\sum_{i=1}^{3} a_i \\,\\delta_{i{\\color{red}{3}}} &=& a_1\\, \\delta_{1{\\color{red}{3}}} + a_2\\, \\delta_{2{\\color{red}{3}}}\u00a0 + a_3 \\, \\delta_{3{\\color{red}{3}}} \\\\
    \n&=& a_1\\cdot 0 + a_2\\cdot 0\u00a0 + a_3 \\cdot 1\\\\
    \n&=& a_{\\color{red}{3}}
    \n\\end{eqnarray}<\/p>\n

    \u3060\u304b\u3089\uff0c$\\color{red}{j = 1, 2, 3}$ \u306e\u3059\u3079\u3066\u306e\u5834\u5408\u306b<\/p>\n

    $$\\sum_{i=1}^{3} a_i \\,\\delta_{i{\\color{red}{j}}} = a_{\\color{red}{j}}$$<\/p>\n

    \u6210\u308a\u7acb\u3063\u3066\u3044\u308b\u306e\u3060\u306a\u3041\uff0c\u3068\u7406\u89e3\u3059\u308b\u3002<\/p>\n

    \u4e09\u89d2\u95a2\u6570\u306e\u300c\u76f4\u4ea4\u6027\u300d<\/h3>\n

    \u30b3\u30b5\u30a4\u30f3\u540c\u58eb<\/h4>\n

    \\begin{eqnarray}
    \n\\int_{-\\pi}^{\\pi} \\cos (m x) \\, \\cos (n x)\\, dx &=& \\frac{1}{2} \\int_{-\\pi}^{\\pi}
    \n\\Bigl\\{\\cos\\bigl((m+n)x\\bigr) + \\cos \\bigl((m-n)x\\bigr)
    \n\\Bigr\\} \\,dx \\\\
    \n&=& \\pi \\delta_{mn} = \\begin{cases}
    \n\\pi & (m = n) \\\\
    \n0\u00a0 & (m \\neq n)
    \n\\end{cases}
    \n\\end{eqnarray} \u3053\u308c\u3092\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8aad\u3080\uff1a\u30b3\u30b5\u30a4\u30f3\u306f\u81ea\u5206\u81ea\u8eab\u3068\u306e\uff08\u5185\u7a4d\u306b\u76f8\u5f53\u3059\u308b\uff09\u7a4d\u5206\u304c\\(\\pi\\)\uff0c\u305d\u308c\u4ee5\u5916\uff08\u3068\u306e\u5185\u7a4d\u306b\u76f8\u5f53\u3059\u308b\u7a4d\u5206\uff09\u306f\u30bc\u30ed\u3002<\/p>\n

    \u88dc\u8db3\uff1a$\\cos (ax)$ \u306e\u7a4d\u5206\u306b\u95a2\u3057\u3066<\/h5>\n

    \u5b66\u751f\u304b\u3089\u8cea\u554f\u304c\u3042\u3063\u305f\u306e\u3067\u3002\u4efb\u610f\u306e\u5b9a\u6570 $a$ \u306b\u5bfe\u3057\u3066<\/p>\n

    $$\\int_{-\\pi}^{\\pi}\\ \\cos (a x)\\, dx = \\biggl[\\frac{\\sin (a x)}{a}\\biggr]_{-\\pi}^{\\pi}$$<\/p>\n

    \u3068\u306a\u308b\u306e\u306f\uff0c$a \\neq 0$ \u306e\u3068\u304d\u3002$a = 0$ \u306e\u3068\u304d\u306b\u306f\u5206\u6bcd\u304c\u30bc\u30ed\u306b\u306a\u308b\u306e\u306f\u56f0\u308b\u306e\u3067\u5225\u9014\uff0c<\/p>\n

    $$\\int_{-\\pi}^{\\pi}\\ \\cos (0\\cdot\u00a0 x)\\, dx = \\int_{-\\pi}^{\\pi} \\ 1\\, dx = \\bigl[x\\bigr]_{-\\pi}^{\\pi}$$<\/p>\n

    \u3053\u306e\u3078\u3093\u304c\u7406\u89e3\u3067\u304d\u308b\u3068<\/p>\n

    \\begin{eqnarray}
    \n\\frac{1}{2} \\int_{-\\pi}^{\\pi}
    \n\\ \\cos \\bigl((m-n)x\\bigr)
    \n\\,dx
    \n&=&\u00a0 \\begin{cases}
    \n\\pi & (m = n) \\\\
    \n0\u00a0 & (m \\neq n)
    \n\\end{cases}
    \n\\end{eqnarray}<\/p>\n

    \u3082\u554f\u984c\u306a\u3044\u3067\u3057\u3087\uff1f<\/p>\n

    \u30b5\u30a4\u30f3\u3068\u30b3\u30b5\u30a4\u30f3<\/h4>\n

    \\begin{eqnarray}
    \n\\int_{-\\pi}^{\\pi} \\sin (m x) \\, \\cos (n x)\\, dx &=& \\frac{1}{2} \\int_{-\\pi}^{\\pi}
    \n\\Bigl\\{\\sin \\bigl((m+n)x\\bigr) + \\sin \\bigl((m-n)x\\bigr)
    \n\\Bigr\\} \\,dx \\\\
    \n&=& \u00a0\u00a0\u00a0 0
    \n\\end{eqnarray}<\/p>\n

    \u3053\u308c\u3092\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8aad\u3080\uff1a\u30b5\u30a4\u30f3\u3068\u30b3\u30b5\u30a4\u30f3\u3068\u306e\uff08\u5185\u7a4d\u306b\u76f8\u5f53\u3059\u308b\uff09\u7a4d\u5206\u306f\u30bc\u30ed\u3002\u88ab\u7a4d\u5206\u95a2\u6570\u304c\u5947\u95a2\u6570\u3068\u306a\u308b\u304b\u3089\uff0c$-\\pi$ \u304b\u3089 $\\pi$ \u307e\u3067\u306e\u7a4d\u5206\u306f\u30bc\u30ed\u306b\u306a\u308b\u3053\u3068\u306f\u7c21\u5358\u3060\u306d\u3002<\/p>\n

    \u30b5\u30a4\u30f3\u540c\u58eb<\/h4>\n

    \\begin{eqnarray}
    \n\\int_{-\\pi}^{\\pi} \\sin (m x) \\, \\sin (n x)\\, dx &=& \\frac{1}{2} \\int_{-\\pi}^{\\pi}
    \n\\Bigl\\{\\cos \\bigl((m-n)x\\bigr) – \\cos \\bigl((m+n)x\\bigr)
    \n\\Bigr\\} \\,dx \\\\
    \n&=&\u00a0 \\pi \\delta_{mn} = \\begin{cases}
    \n\\pi & (m = n) \\\\
    \n0\u00a0 & (m \\neq n)
    \n\\end{cases}
    \n\\end{eqnarray}\u3053\u308c\u3092\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8aad\u3080\uff1a\u30b5\u30a4\u30f3\u306f\u81ea\u5206\u81ea\u8eab\u3068\u306e\uff08\u5185\u7a4d\u306b\u76f8\u5f53\u3059\u308b\uff09\u7a4d\u5206\u304c\\(\\pi\\)\uff0c\u305d\u308c\u4ee5\u5916\uff08\u3068\u306e\u5185\u7a4d\u306b\u76f8\u5f53\u3059\u308b\u7a4d\u5206\uff09\u306f\u30bc\u30ed\u3002<\/p>\n

    \u304b\u305f\u3084\u57fa\u672c\u30d9\u30af\u30c8\u30eb\u306f3\u6b21\u5143\u30d9\u30af\u30c8\u30eb\u306e\u5185\u7a4d\uff0c\u304b\u305f\u3084\u4e09\u89d2\u95a2\u6570\u306f\u533a\u9593 \\(-\\pi \\le x \\le \\pi \\) \u306e\u7a4d\u5206\u3067\u306f\u3042\u308b\u304c\uff0c\u540c\u3058\u3082\u306e\u540c\u58eb\u306e\u5834\u5408\u306f\u5024\u3092\u6301\u3061\uff0c\u305d\u308c\u4ee5\u5916\u306e\u5834\u5408\u306f\u30bc\u30ed\u3068\u3044\u3046\u610f\u5473\u3067\u300c\u76f4\u4ea4\u6027\u300d\u3068\u3044\u3046\u3053\u3068\u304c\u7406\u89e3\u3067\u304d\u308b\uff0c\u3068\u601d\u3044\u307e\u3059\u304c\u3069\u3046\u3067\u3057\u3087\u3046\uff1f<\/p>\n

    \u4e09\u89d2\u95a2\u6570\u306e\u76f4\u4ea4\u6027\u3092\u5229\u7528\u3057\u3066\u30d5\u30fc\u30ea\u30a8\u4fc2\u6570\u3092\u6c42\u3081\u308b<\/h3>\n

    $$ f(x) = \\frac{a_0}{2} + \\sum_{n=1}^{\\infty} \\bigl( a_n \\cos (n x) + b_n \\sin (n x) \\bigr) $$ \u306e\u5f0f\u306e\u4e21\u8fba\u306b \\(\\displaystyle \\int_{-\\pi}^{\\pi}\u00a0 \\, \\cos (m x) \\, dx\\) \u3092\u300c\u304b\u3051\u308b\u300d\u3068…
    \n$$ m = 0: \\quad \\int_{-\\pi}^{\\pi} \\, f(x) \\, \\cos (m x)\\, dx = \\pi\\, a_0$$
    \n$$ m \\geq 1: \\quad \\int_{-\\pi}^{\\pi} \\,f(x) \\, \\cos (m x)\\, dx = \\sum_{n=1}^{\\infty} a_n\\, \\pi \\delta_{nm} = \\pi\\, a_m$$<\/p>\n

    \u540c\u69d8\u306b\uff0c
    \n$$ m \\geq 1: \\quad \\int_{-\\pi}^{\\pi} \\,f(x) \\, \\sin (m x)\\, dx = \\sum_{n=1}^{\\infty} b_n\\, \\pi \\delta_{nm} = \\pi\\, b_m$$<\/p>\n

    \u88dc\u8db3\uff1a\u30af\u30ed\u30cd\u30c3\u30ab\u30fc\u306e\u30c7\u30eb\u30bf\u304c\u3089\u307f\u306e\u8a08\u7b97\u306b\u95a2\u3057\u3066<\/h4>\n

    \u3053\u3053\u3082\u5b66\u751f\u304b\u3089\u8cea\u554f\u304c\u3042\u308a\u305d\u3046\u306a\u306e\u3067\u3002$\\displaystyle \\sum_{n=1}^{\\infty} a_n\\, \\delta_{nm} = a_m$ \u3092\u7406\u89e3\u3059\u308b\u306b\u306f\uff0c\u305f\u3068\u3048\u3070\u4ee5\u4e0b\u306e\u3088\u3046\u306b\uff1a<\/p>\n

    \\begin{eqnarray}
    \n\\sum_{n=1}^{\\infty} a_n\\, \\delta_{nm} &=& \\sum_{n=1}^{m -1} a_n\\, \\delta_{nm} + a_m\\, \\delta_{mm} + \\sum_{n=m+1}^{\\infty} a_n\\, \\delta_{nm} \\\\
    \n&=& \\sum_{n=1}^{m -1} a_n\\cdot 0 + a_m \\cdot 1 + \\sum_{n=m+1}^{\\infty} a_n\\cdot 0 \\\\
    \n&=& a_m
    \n\\end{eqnarray}<\/p>\n

     <\/p>\n

    \u30d5\u30fc\u30ea\u30a8\u7d1a\u6570\u5c55\u958b\u306e\u307e\u3068\u3081<\/h3>\n

    \u4ee5\u4e0a\u3092\u307e\u3068\u3081\u308b\u3068\u6b21\u306e\u3088\u3046\u306b\u306a\u308b\u3002\u4ee5\u5f8c\u306f\u3053\u308c\u3092\u516c\u5f0f\u3068\u3057\u3066\u4f7f\u3063\u3066\uff0c\u30d5\u30fc\u30ea\u30a8\u7d1a\u6570\u5c55\u958b\u3092\u884c\u3063\u3066\u304f\u3060\u3055\u3044\u3002
    \n$$ f(x) = \\frac{a_0}{2} + \\sum_{n=1}^{\\infty} \\bigl( a_n \\cos (n x) + b_n \\sin (n x) \\bigr) $$
    \n$$a_n = \\frac{1}{\\pi} \\int_{-\\pi}^{\\pi} f(x) \\cos (n x) \\, dx $$
    \n$$b_n = \\frac{1}{\\pi} \\int_{-\\pi}^{\\pi} f(x) \\sin (n x) \\, dx $$<\/p>\n

    \u4ee5\u4e0a\u306e\u95a2\u4fc2\u30923\u6b21\u5143\u30d9\u30af\u30c8\u30eb\u306e\u4ee5\u4e0b\u306e\u95a2\u4fc2\u3068\u6bd4\u3079\u3066\u985e\u4f3c\u6027\u3092\u5473\u308f\u3063\u3066\u307f\u308b\u306e\u3082\u8208\u5473\u6df1\u3044\u3002
    \n$$ \\boldsymbol{a} = \\sum_{i=1}^{3} a_i\\, \\boldsymbol{e}_i $$ $$ a_i = \\boldsymbol{a}\\cdot\\boldsymbol{e}_i\u00a0\u00a0 $$<\/p>\n

    \u30d5\u30fc\u30ea\u30a8\u5c55\u958b\u3059\u308b\u95a2\u6570 $f(x)$ \u304c\u3061\u3087\u3046\u3069 $\\boldsymbol{a}$ \u306b\uff0c\u30d5\u30fc\u30ea\u30a8\u7d1a\u6570\u306e \\(\\cos (n x), \\ \\sin (n x)\\) \u304c\u3061\u3087\u3046\u3069\u57fa\u672c\u30d9\u30af\u30c8\u30eb \\(\\boldsymbol{e}_i \\) \u306e\u5f79\u5272\u3092\uff0c\u30d5\u30fc\u30ea\u30a8\u4fc2\u6570 \\( a_n, \\ b_n\\) \u304c\u30d9\u30af\u30c8\u30eb\u306e\u6210\u5206 \\(a_i \\) \u306e\u5f79\u5272\u3092\u62c5\u3063\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308b\u3067\u3057\u3087\u3046\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

    \u533a\u9593 \\(-\\pi \\le x \\le \\pi\\) \u3067\u5b9a\u7fa9\u3055\u308c\u305f\u95a2\u6570 \\(f(x)\\) \u306f\uff0c\u305d\u308c\u304c\u3069\u3093\u306a\u95a2\u6570\u3067\u3042\u3063\u3066\u3082\uff08\u533a\u9593\u5916\u3067\u306f\uff0c\u5468\u671f \\( 2\\pi \\) \u306e\u5468\u671f\u95a2\u6570\u3068\u307f\u306a\u3057\u3066\uff09\uff0c\u4e09\u89d2\u95a2\u6570 \\( \\cos, \\ \\sin \\) \u306e\u91cd\u306d\u5408\u308f\u305b\u3067\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/p>

    \u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":33,"featured_media":0,"parent":2230,"menu_order":1,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-2362","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\/2362","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=2362"}],"version-history":[{"count":19,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/2362\/revisions"}],"predecessor-version":[{"id":10584,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/2362\/revisions\/10584"}],"up":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/2230"}],"wp:attachment":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/media?parent=2362"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}