{"id":2364,"date":"2022-02-26T10:45:38","date_gmt":"2022-02-26T01:45:38","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=2364"},"modified":"2025-07-27T13:30:47","modified_gmt":"2025-07-27T04:30:47","slug":"%e4%bb%bb%e6%84%8f%e3%81%ae%e5%91%a8%e6%9c%9f%e3%82%92%e3%82%82%e3%81%a4%e9%96%a2%e6%95%b0%e3%81%ae%e3%83%95%e3%83%bc%e3%83%aa%e3%82%a8%e7%b4%9a%e6%95%b0%e5%b1%95%e9%96%8b","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\/%e4%bb%bb%e6%84%8f%e3%81%ae%e5%91%a8%e6%9c%9f%e3%82%92%e3%82%82%e3%81%a4%e9%96%a2%e6%95%b0%e3%81%ae%e3%83%95%e3%83%bc%e3%83%aa%e3%82%a8%e7%b4%9a%e6%95%b0%e5%b1%95%e9%96%8b\/","title":{"rendered":"\u4efb\u610f\u306e\u5468\u671f\u3092\u3082\u3064\u95a2\u6570\u306e\u30d5\u30fc\u30ea\u30a8\u7d1a\u6570\u5c55\u958b"},"content":{"rendered":"

\u30d5\u30fc\u30ea\u30a8\u7d1a\u6570\u306e\u5c0e\u5165\u3067\u306f\uff0c\u533a\u9593 \\( -\\pi \\le x \\le \\pi \\) \u3067\u5b9a\u7fa9\u3055\u308c\u305f\u95a2\u6570 \\(f(x)\\) \u304c\uff0c\u305d\u306e\u533a\u9593\u306e\u5916\u3067\u306f\u5468\u671f \\(2\\pi\\) \u306e\u5468\u671f\u95a2\u6570\u3067\u3042\u308b\u3068\u3057\u305f\u3002<\/p>\n

\u5468\u671f \\(2\\pi\\) \u306e\u6c7a\u3081\u6253\u3061\u3067\u306f\u306a\u304f\uff0c\u4efb\u610f\u306e\u5468\u671f\u3092\u3082\u3064\u95a2\u6570\u306e\u5834\u5408\u306f\u3069\u3046\u306a\u308b\u304b\uff0c\u3068\u3044\u3046\u8a71\u3002<\/p>\n

\u533a\u9593 \\( -L \\le x \\le L\\) \u3067\u5b9a\u7fa9\u3055\u308c\u305f\u95a2\u6570 \\(f(x)\\) \u304c\u533a\u9593\u5916\u3067\u306f\u5468\u671f \\(2 L\\) \u306e\u5468\u671f\u95a2\u6570\u3067\u3042\u308b\u5834\u5408\uff0c\u305d\u306e\u30d5\u30fc\u30ea\u30a8\u7d1a\u6570\u5c55\u958b\u306f…
\n<\/p>\n

\n

\u5148\u306b\u307e\u3068\u3081<\/h3>\n

\u5148\u306b\u7b54\u3048\u3092\u66f8\u3044\u3066\u304a\u304f\u3002\u533a\u9593 \\( -L \\le x \\le L\\) \u3067\u5b9a\u7fa9\u3055\u308c\u305f\u95a2\u6570 \\(f(x)\\) \u304c\u533a\u9593\u5916\u3067\u306f\u5468\u671f \\(2 L\\) \u306e\u5468\u671f\u95a2\u6570\u3067\u3042\u308b\u5834\u5408\uff0c\u305d\u306e\u30d5\u30fc\u30ea\u30a8\u7d1a\u6570\u5c55\u958b\u306f
\n$$ f(x) = \\frac{a_0}{2} + \\sum_{n=1}^{\\infty} \\biggl( a_n \\cos \\left(\\frac{n\\pi x}{L} \\right) + b_n \\sin \\left(\\frac{n\\pi x}{L} \\right) \\biggr) $$
\n$$a_n = \\frac{1}{L} \\int_{-L}^{L} f(x) \\cos \\left(\\frac{n\\pi x}{L} \\right) \\, dx $$
\n$$b_n = \\frac{1}{L} \\int_{-L}^{L} f(x) \\sin \\left(\\frac{n\\pi x}{L} \\right) \\, dx $$<\/p>\n

\u4ee5\u4e0b\u306f\uff0c\u3053\u3046\u306a\u308b\u7406\u7531\u3002<\/p>\n

 <\/p>\n

\u5468\u671f \\( 2L\\) \u306e\u5468\u671f\u95a2\u6570<\/h3>\n

 <\/p>\n

\u533a\u9593 \\( -L \\le x \\le L\\) \u3067\u5b9a\u7fa9\u3055\u308c\u305f\u95a2\u6570 \\(f(x) \\) \u304c\uff0c\u305d\u306e\u533a\u9593\u5916\u3067\u306f\u5468\u671f \\(2 L\\) \u306e\u5468\u671f\u95a2\u6570\u3067\u3042\u308b\u3068\u3057\uff0c\u3053\u306e\u95a2\u6570\u3092\u30d5\u30fc\u30ea\u30a8\u7d1a\u6570\u5c55\u958b\u3059\u308b\u3002<\/p>\n

\u5468\u671f \\(2\\pi\\) \u306e\u5834\u5408\u306e\u516c\u5f0f\u304b\u3089\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u3057\u3066\u5909\u6570\u3092\u7f6e\u304d\u63db\u3048\u308b\u3002<\/p>\n

\u307e\u305a\uff0c$$ -\\pi \\le {\\color{blue}{x}} \\le \\pi $$ \u3092 \\(\\pi\\) \u3067\u308f\u3063\u3066 $$ -1 \\le \\frac{1}{\\pi}{\\color{blue}{x} }\\le 1 $$ \u305d\u3057\u3066 \\(L\\) \u3092\u304b\u3051\u3066 $$ -L \\le \\frac{L}{\\pi} {\\color{blue}{x}} \\le L $$
\n$$ \\frac{L}{\\pi} {\\color{blue}{x}}\\Rightarrow {\\color{red}{x}} \\quad\\mbox{or}\\quad {\\color{blue}{x} }\\Rightarrow \\frac{\\pi}{L} {\\color{red}{x}}$$ \u3068\u7f6e\u304d\u63db\u3048\u308b\u3068 $$ -L \\le {\\color{red}{x} }\\le L$$<\/p>\n

\u3064\u307e\u308a\uff0c\u4efb\u610f\u306e\u5468\u671f \\(2L\\) \u306e\u5468\u671f\u95a2\u6570\u306e\u30d5\u30fc\u30ea\u30a8\u7d1a\u6570\u306f\uff0c\u5468\u671f \\(2\\pi\\) \u306e\u5834\u5408\u306e\u4ee5\u4e0b\u306e\u5f0f<\/p>\n

$$ f(x) = \\frac{a_0}{2} + \\sum_{n=1}^{\\infty} \\biggl( a_n \\cos (n {\\color{blue}{x}})\u00a0 + b_n \\sin (n {\\color{blue}{x}} )\\biggr) $$
\n$$a_n = \\frac{1}{\\pi} \\int_{-\\pi}^{\\pi} f(x) \\cos (n {\\color{blue}{x}}) \\, d{\\color{blue}{x}} $$
\n$$b_n = \\frac{1}{\\pi} \\int_{-\\pi}^{\\pi} f(x) \\sin (n {\\color{blue}{x}}) \\, d{\\color{blue}{x}} $$
\n\u3067\uff0c$${\\color{blue}{x}} \\Rightarrow \\frac{\\pi}{L} {\\color{red}{x}}, \\quad d{\\color{blue}{x}} \\Rightarrow \\frac{\\pi}{L} d{\\color{red}{x}}$$ \u3068\u7f6e\u304d\u63db\u3048\u308c\u3070\u3088\u304f\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308b\u3002
\n$$ f(x) = \\frac{a_0}{2} + \\sum_{n=1}^{\\infty} \\biggl( a_n \\cos \\left(\\frac{n \\pi \u00a0{\\color{red}{x}}}{L}\\right) + b_n \\sin \\left(\\frac{n \\pi {\\color{red}{x}}}{L}\\right) \\biggr) $$
\n$$a_n = \\frac{1}{\\pi} \\int_{-L}^{L} f(x) \\cos \\left(\\frac{n \\pi {\\color{red}{x}} }{L}\\right) \\, \\frac{\\pi}{L} d{\\color{red}{x}} $$
\n$$b_n = \\frac{1}{\\pi} \\int_{-L}^{L} f(x) \\sin \\left(\\frac{n \\pi {\\color{red}{x}}}{L} \\right)\\, \\frac{\\pi}{L} d{\\color{red}{x}} $$<\/p>\n","protected":false},"excerpt":{"rendered":"

\u30d5\u30fc\u30ea\u30a8\u7d1a\u6570\u306e\u5c0e\u5165\u3067\u306f\uff0c\u533a\u9593 \\( -\\pi \\le x \\le \\pi \\) \u3067\u5b9a\u7fa9\u3055\u308c\u305f\u95a2\u6570 \\(f(x)\\) \u304c\uff0c\u305d\u306e\u533a\u9593\u306e\u5916\u3067\u306f\u5468\u671f \\(2\\pi\\) \u306e\u5468\u671f\u95a2\u6570\u3067\u3042\u308b\u3068\u3057\u305f\u3002<\/p>\n

\u5468\u671f \\(2\\pi\\) \u306e\u6c7a\u3081\u6253\u3061\u3067\u306f\u306a\u304f\uff0c\u4efb\u610f\u306e\u5468\u671f\u3092\u3082\u3064\u95a2\u6570\u306e\u5834\u5408\u306f\u3069\u3046\u306a\u308b\u304b\uff0c\u3068\u3044\u3046\u8a71\u3002<\/p>\n

\u533a\u9593 \\( -L \\le x \\le L\\) \u3067\u5b9a\u7fa9\u3055\u308c\u305f\u95a2\u6570 \\(f(x)\\) \u304c\u533a\u9593\u5916\u3067\u306f\u5468\u671f \\(2 L\\) \u306e\u5468\u671f\u95a2\u6570\u3067\u3042\u308b\u5834\u5408\uff0c\u305d\u306e\u30d5\u30fc\u30ea\u30a8\u7d1a\u6570\u5c55\u958b\u306f…<\/p>

\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":33,"featured_media":0,"parent":2230,"menu_order":2,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-2364","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\/2364","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=2364"}],"version-history":[{"count":9,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/2364\/revisions"}],"predecessor-version":[{"id":10580,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/2364\/revisions\/10580"}],"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=2364"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}