[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/jp\/wiki4\/2020\/10\/25\/%e3%83%ab%e3%83%b3%e3%82%b2%e3%81%ae%e5%ae%9a%e7%90%86-wikipedia\/#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/jp\/wiki4\/2020\/10\/25\/%e3%83%ab%e3%83%b3%e3%82%b2%e3%81%ae%e5%ae%9a%e7%90%86-wikipedia\/","headline":"\u30eb\u30f3\u30b2\u306e\u5b9a\u7406 &#8211; Wikipedia","name":"\u30eb\u30f3\u30b2\u306e\u5b9a\u7406 &#8211; Wikipedia","description":"\u9752\u8272\u306e\u30b3\u30f3\u30d1\u30af\u30c8\u96c6\u5408\u3068\u5404\u3005\u306e\u7a74\u306e\u4e2d\u306e\u70b9\u4e0a\u3067\u4e0e\u3048\u3089\u308c\u305f\u6b63\u5247\u51fd\u6570 f \u304c\u4e0e\u3048\u3089\u308c\u308b\u3068\u3001\u3053\u308c\u3089\u306e 3\u3064\u306e\u70b9\u3067\u306e\u307f\u6975\u3092\u6301\u3064\u6709\u7406\u95a2\u6570\u306b\u3088\u308a f \u3092\u8fd1\u4f3c\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002 \u8907\u7d20\u89e3\u6790\u3067\u306f\u3001\u30eb\u30f3\u30b2\u306e\u5b9a\u7406\uff08\u82f1: Runge&#8217;s theorem\uff09\uff08\u30eb\u30f3\u30b2\u306e\u8fd1\u4f3c\u5b9a\u7406\uff08\u82f1: Runge&#8217;s approximation theorem\uff09\u3068\u3057\u3066\u3082\u77e5\u3089\u308c\u3066\u3044\u308b\uff09\u306f\u30011885\u5e74\u3001\u6700\u521d\u306b\u3053\u306e\u5b9a\u7406\u3092\u8a3c\u660e\u3057\u305f\u30c9\u30a4\u30c4\u306e\u6570\u5b66\u8005\u30ab\u30fc\u30eb\u30fb\u30eb\u30f3\u30b2\u306e\u540d\u524d\u306b\u56e0\u3080\u3002\u3053\u306e\u5b9a\u7406\u306f\u4ee5\u4e0b\u306e\u5185\u5bb9\u3067\u3042\u308b\u3002 C \u3092\u8907\u7d20\u6570\u306e\u96c6\u5408\u3001K \u3092 C \u306e\u30b3\u30f3\u30d1\u30af\u30c8\u90e8\u5206\u96c6\u5408\u3001f \u3092 K \u3092\u542b\u3080\u958b\u96c6\u5408\u4e0a\u3067\u6b63\u5247\u306a\u51fd\u6570\u3068\u3059\u308b\u3002","datePublished":"2020-10-25","dateModified":"2020-10-25","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/jp\/wiki4\/author\/lordneo\/#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/jp\/wiki4\/author\/lordneo\/","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/e\/e1\/Runge_theorem.svg\/320px-Runge_theorem.svg.png","url":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/e\/e1\/Runge_theorem.svg\/320px-Runge_theorem.svg.png","height":"240","width":"320"},"url":"https:\/\/wiki.edu.vn\/jp\/wiki4\/2020\/10\/25\/%e3%83%ab%e3%83%b3%e3%82%b2%e3%81%ae%e5%ae%9a%e7%90%86-wikipedia\/","wordCount":2023,"articleBody":"  \u9752\u8272\u306e\u30b3\u30f3\u30d1\u30af\u30c8\u96c6\u5408\u3068\u5404\u3005\u306e\u7a74\u306e\u4e2d\u306e\u70b9\u4e0a\u3067\u4e0e\u3048\u3089\u308c\u305f\u6b63\u5247\u51fd\u6570 f \u304c\u4e0e\u3048\u3089\u308c\u308b\u3068\u3001\u3053\u308c\u3089\u306e 3\u3064\u306e\u70b9\u3067\u306e\u307f\u6975\u3092\u6301\u3064\u6709\u7406\u95a2\u6570\u306b\u3088\u308a f \u3092\u8fd1\u4f3c\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u8907\u7d20\u89e3\u6790\u3067\u306f\u3001\u30eb\u30f3\u30b2\u306e\u5b9a\u7406\uff08\u82f1: Runge&#8217;s theorem\uff09\uff08\u30eb\u30f3\u30b2\u306e\u8fd1\u4f3c\u5b9a\u7406\uff08\u82f1: Runge&#8217;s approximation theorem\uff09\u3068\u3057\u3066\u3082\u77e5\u3089\u308c\u3066\u3044\u308b\uff09\u306f\u30011885\u5e74\u3001\u6700\u521d\u306b\u3053\u306e\u5b9a\u7406\u3092\u8a3c\u660e\u3057\u305f\u30c9\u30a4\u30c4\u306e\u6570\u5b66\u8005\u30ab\u30fc\u30eb\u30fb\u30eb\u30f3\u30b2\u306e\u540d\u524d\u306b\u56e0\u3080\u3002\u3053\u306e\u5b9a\u7406\u306f\u4ee5\u4e0b\u306e\u5185\u5bb9\u3067\u3042\u308b\u3002C \u3092\u8907\u7d20\u6570\u306e\u96c6\u5408\u3001K \u3092 C \u306e\u30b3\u30f3\u30d1\u30af\u30c8\u90e8\u5206\u96c6\u5408\u3001f \u3092 K \u3092\u542b\u3080\u958b\u96c6\u5408\u4e0a\u3067\u6b63\u5247\u306a\u51fd\u6570\u3068\u3059\u308b\u3002C\u2216K{displaystyle mathbb {C} backslash K} \u4e2d\u306e\u3059\u3079\u3066\u306e\u6709\u754c\u9023\u7d50\u306a\u96c6\u5408\u306b\u3064\u3044\u3066\u3001\u305d\u308c\u305e\u308c\u306e\u5143\u306e\u8907\u7d20\u6570\u3092\u5c11\u306a\u304f\u3068\u3082\u3072\u3068\u3064\u542b\u3080\u3088\u3046\u306a\u96c6\u5408\u3092 A \u3068\u3059\u308b\u3068\u3001K \u4e0a\u306e f \u3078\u4e00\u69d8\u53ce\u675f\u3059\u308b\u6709\u7406\u51fd\u6570\u5217 (rn)n\u2208N{displaystyle (r_{n})_{nin mathbb {N} }} \u304c\u5b58\u5728\u3057\u3001\u51fd\u6570 (rn)n\u2208N{displaystyle (r_{n})_{nin mathbb {N} }} \u306e\u3059\u3079\u3066\u306e\u6975\u306f A \u306e\u5143\u3067\u3042\u308b\u3002A \u306e\u3059\u3079\u3066\u306e\u8907\u7d20\u6570\u304c\u6709\u7406\u51fd\u6570\u5217 (rn)n\u2208N{displaystyle (r_{n})_{nin mathbb {N} }} \u306e\u6975\u3068\u306a\u308b\u308f\u3051\u3067\u306f\u306a\u3044\u3053\u3068\u306b\u6ce8\u610f\u3059\u308b\u3002\u51fd\u6570\u5217\u306e\u8981\u7d20 (rn)n\u2208N{displaystyle (r_{n})_{nin mathbb {N} }} \u304c\u3059\u3079\u3066\u6975\u3092\u6301\u3061\u3001\u305d\u308c\u3089\u304c A \u306e\u4e2d\u306b\u3042\u308b\u3053\u3068\u3057\u304b\u5206\u304b\u3089\u306a\u3044\u3002\u3053\u306e\u5b9a\u7406\u304c\u975e\u5e38\u306b\u5f37\u529b\u3067\u3042\u308b\u70b9\u306f\u3001\u96c6\u5408 A \u3092\u4efb\u610f\u306b\u9078\u629e\u3067\u304d\u308b\u3053\u3068\u306b\u3042\u308b\u3002\u8a00\u3044\u63db\u3048\u308b\u3068\u3001C\u2216K{displaystyle mathbb {C} backslash K} \u306e\u6709\u754c\u9023\u7d50\u306a\u6210\u5206\u306e\u4e2d\u304b\u3089\u4efb\u610f\u306e\u8907\u7d20\u6570\u3092\u9078\u3076\u3053\u3068\u304c\u3067\u304d\u3001\u9078\u3093\u3060\u6570\u306e\u307f\u304c\u6975\u3068\u306a\u308b\u6709\u7406\u51fd\u6570\u5217\u306e\u5b58\u5728\u304c\u5b9a\u7406\u304b\u3089\u4fdd\u8a3c\u3055\u308c\u308b\u3002C\u2216K{displaystyle mathbb {C} backslash K} \u304c\u9023\u7d50\u96c6\u5408\uff08K \u304c\u5358\u9023\u7d50\u3067\u3042\u308b\u3053\u3068\u3068\u540c\u5024\uff09\u3067\u3042\u308b\u7279\u5225\u306a\u5834\u5408\u306f\u3001\u5b9a\u7406\u306e\u96c6\u5408 A \u306f\u7a7a\u96c6\u5408\u3068\u306a\u308b\u3002\u6975\u3092\u3082\u305f\u306a\u3044\u6709\u7406\u51fd\u6570\u306f\u5358\u306b\u591a\u9805\u5f0f\u3067\u3042\u308b\u306e\u3067\u3001\u6b21\u306e\u7cfb\u3092\u5f97\u308b\u3002C\u2216K{displaystyle mathbb {C} backslash K} \u304c\u9023\u7d50\u96c6\u5408\u3067\u3042\u308b\u3088\u3046\u306a C \u306e\u30b3\u30f3\u30d1\u30af\u30c8\u90e8\u5206\u96c6\u5408\u3092 K \u3068\u3057\u3066\u3001f \u304c K \u4e0a\u306e\u6b63\u5247\u51fd\u6570\u3067\u3042\u308c\u3070\u3001K \u4e0a\u3067 f \u306b\u4e00\u69d8\u53ce\u675f\u3059\u308b\u591a\u9805\u5f0f\u306e\u5217 (pn){displaystyle (p_{n})} \u304c\u5b58\u5728\u3059\u308b\u3002\u30eb\u30f3\u30b2\u306e\u5b9a\u7406\u306f\u6b21\u306e\u3088\u3046\u306b\u4e00\u822c\u5316\u3055\u308c\u308b\u3002A \u3092\u30ea\u30fc\u30de\u30f3\u7403\u9762 C\u222a{\u221e} \u306e\u90e8\u5206\u96c6\u5408\u3068\u3057\u3001A \u304c K \u306e\u975e\u6709\u754c\u306a\u9023\u7d50\u6210\u5206\uff08\u221e \u3092\u542b\u3080\uff09\u3068\u4ea4\u308f\u308b\u3068\u3059\u308b\u3068\u3001\u4e0a\u306e\u5b9a\u5f0f\u5316\u306b\u304a\u3044\u3066\u3001\u6709\u7406\u51fd\u6570\u306f\u7121\u9650\u9060\u70b9\u306b\u6975\u3092\u6301\u3064\u3053\u3068\u304c\u5206\u304b\u308b\u3002\u4e00\u65b9\u3001\u3055\u3089\u306b\u4e00\u822c\u7684\u306a\u5b9a\u5f0f\u5316\u306e\u4e2d\u3067\u306f\u3001\u6975\u306f K \u306e\u975e\u6709\u754c\u306a\u9023\u7d50\u6210\u5206\u306e\u3069\u3053\u306b\u3067\u3082\u9078\u3076\u3053\u3068\u304c\u3067\u304d\u308b\u3002Sarason (1998)\u3067\u4e0e\u3048\u3089\u308c\u305f\u57fa\u672c\u7684\u306a\u8a3c\u660e\u306f\u3001\u6b21\u306e\u3088\u3046\u306a\u8a3c\u660e\u3067\u3042\u308b\u3002\u9589\u3067\u533a\u5206\u7dda\u578b\u306a K \u3092\u542b\u3080\u958b\u96c6\u5408\u306e\u5468\u56f2 \u0393 \u304c\u5b58\u5728\u3059\u308b\u3002\u30b3\u30fc\u30b7\u30fc\u306e\u7a4d\u5206\u5b9a\u7406\u306b\u3088\u308a\u3001K \u306e\u5143 w \u306b\u3064\u3044\u3066\u3001f(w)=12\u03c0i\u222b\u0393f(z)dzz\u2212w{displaystyle f(w)={1 over 2pi i}int _{Gamma }{f(z),dz over z-w}}\u3067\u3042\u308b\u3002\u30ea\u30fc\u30de\u30f3\u8fd1\u4f3c\u548c\u306f\u3001K \u4e0a\u306e\u5468\u56de\u7a4d\u5206\u3092\u4e00\u69d8\u306b\u8fd1\u4f3c\u3059\u308b\u3053\u3068\u306b\u4f7f\u3048\u308b\u3002\u548c\u306e\u5404\u3005\u306e\u9805\u306f\u3001\u7a4d\u5206\u7d4c\u8def\u4e0a\u306e\u4efb\u610f\u306e\u70b9 z \u306b\u5bfe\u3057\u3066 (z \u2212 w)\u22121 \u306e\u30b9\u30ab\u30e9\u30fc\u500d\u3067\u3042\u308b\u3002\u3053\u308c\u306b\u3088\u3063\u3066 \u0393 \u4e0a\u306b\u6975\u3092\u6301\u3064\u6709\u7406\u51fd\u6570\u3067\u4e00\u69d8\u306b\u8fd1\u4f3c\u3067\u304d\u308b\u3002\u3053\u308c\u3092 K \u306e\u88dc\u96c6\u5408\u306e\u5404\u6210\u5206\u306b\u5bfe\u3059\u308b\u7279\u5b9a\u306e\u70b9\u3067\u6975\u3092\u6301\u3064\u3088\u3046\u306a\u8fd1\u4f3c\u3078\u5909\u5f62\u3059\u308b\u306b\u306f\u3001 (z \u2212 w)\u22121 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\u4e0a\u3067\u3082\u3068\u306e\u51fd\u6570\u306b\u4e00\u69d8\u306b\u8fd1\u3044\u6709\u7406\u51fd\u6570\u3092\u4e0e\u3048\u308b\u3088\u3046\u306b\u3001\u7d1a\u6570\u5c55\u958b\u3092\u6253\u3061\u5207\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002z \u304b\u3089 z0 \u3078\u306e\u7d4c\u8def\u306b\u305d\u3063\u3066\u9032\u3080\u3068\u3001\u3082\u3068\u306e\u51fd\u6570 (z \u2212 w)\u22121 \u306f z0 \u3067\u306e\u307f\u6975\u3092\u6301\u3064\u6709\u7406\u51fd\u6570\u3092\u4e0e\u3048\u308b\u3088\u3046\u306b\u5909\u5f62\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002z0 \u304c\u7121\u9650\u9060\u70b9\u3067\u3042\u308c\u3070\u3001\u4e0a\u306e\u624b\u9806\u306b\u3088\u308a\u3001\u6709\u7406\u51fd\u6570 (z \u2212 w)\u22121 \u3092\u3001R > 0 \u3067\u6975\u3092\u6301\u3064\u6709\u7406\u51fd\u6570 g \u3067\u8fd1\u4f3c\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u3053\u3053\u3067 R \u306f K \u306e\u3069\u306e\u5143\u3082 w < R \u3068\u306a\u308b\u3088\u3046\u306a\u5341\u5206\u306b\u5927\u304d\u306a\u5024\u3067\u3042\u308b\u3002 g \u306e 0 \u8fd1\u508d\u3067\u306e\u30c6\u30a4\u30e9\u30fc\u7d1a\u6570\u5c55\u958b\u306f\u3001K \u4e0a\u306e\u591a\u9805\u5f0f\u8fd1\u4f3c\u3092\u4e0e\u3048\u308b\u3053\u3068\u306b\u3088\u308a\u6253\u3061\u5207\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u53c2\u7167\u9805\u76ee[\u7de8\u96c6]\u53c2\u8003\u6587\u732e[\u7de8\u96c6]Conway, John B. (1997), A Course in Functional Analysis (2nd ed.), Springer, ISBN 0-387-97245-5\u00a0Greene, Robert E.; Krantz, Steven G. (2002), Function Theory of One Complex Variable (2nd ed.), American Mathematical Society, ISBN 0-8218-2905-X\u00a0Sarason, Donald (1998), Notes on complex function theory, Texts and Readings in Mathematics, 5, Hindustan Book Agency, pp.\u00a0108-115, ISBN 81-85931-19-4\u00a0\u5916\u90e8\u30ea\u30f3\u30af[\u7de8\u96c6]"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki4\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki4\/2020\/10\/25\/%e3%83%ab%e3%83%b3%e3%82%b2%e3%81%ae%e5%ae%9a%e7%90%86-wikipedia\/#breadcrumbitem","name":"\u30eb\u30f3\u30b2\u306e\u5b9a\u7406 &#8211; Wikipedia"}}]}]