{"id":597,"date":"2013-02-02T07:44:10","date_gmt":"2013-02-01T22:44:10","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=597"},"modified":"2021-03-18T15:20:25","modified_gmt":"2021-03-18T06:20:25","slug":"tkr200701","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tkr200701\/","title":{"rendered":"\u6771\u5927\u7406\u7cfb2007\uff1a\u7b2c1\u554f"},"content":{"rendered":"<hr \/>\n<p>\\(n\\) \u3068 \\(k\\) \u3092\u6b63\u306e\u6574\u6570\u3068\u3057, \\(P(x)\\) \u3092\u6b21\u6570\u304c \\(n\\) \u4ee5\u4e0a\u306e\u6574\u5f0f\u3068\u3059\u308b.\r\n\u6574\u5f0f \\((1+x)^k P(x)\\) \u306e \\(n\\) \u6b21\u4ee5\u4e0b\u306e\u9805\u306e\u4fc2\u6570\u304c\u3059\u3079\u3066\u6574\u6570\u306a\u3089\u3070,\r\n\\(P(x)\\) \u306e \\(n\\) \u6b21\u4ee5\u4e0b\u306e\u9805\u306e\u4fc2\u6570\u306f\u3059\u3079\u3066\u6574\u6570\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u305b.\r\n\u305f\u3060\u3057, \u5b9a\u6570\u9805\u306b\u3064\u3044\u3066\u306f, \u9805\u305d\u308c\u81ea\u8eab\u3092\u4fc2\u6570\u3068\u307f\u306a\u3059.<\/p>\r\n<hr \/>\r\n<!--more-->\r\n<h2>\u3010 \u89e3 \u7b54 \u3011<\/h2>\r\n<p>\\(P(x) = a _ m x^m + \\cdots +a _ n x^n + \\cdots + a _ 1 x +a _ 0\\) \uff08 \\(m\\) \u306f \\(n\\) \u4ee5\u4e0a\u306e\u6574\u6570\uff09\u3068\u304a\u304f.<br \/>\r\n\u307e\u305f\r\n\\[\\begin{align}\r\nQ _ k (x) & = (1+x)^k P(x) \\\\\r\n& = b _ {k, m+k} (k) x^{m+k} + \\cdots + b _ {k, n} + \\cdots + b _ {k, 1} x + b _ {k, 0}\r\n\\end{align}\\]\r\n\u3068\u304a\u304f.<br \/>\r\n\u3053\u3053\u3067\r\n\\[\\begin{align}\r\nQ _ k (x) & = (1+x) Q _ {k-1} (x) \\\\\r\n& = (1+x) \\left( \\cdots + b _ {k-1, n} x^n + b _ {k-1, n-1} x^{n-1} + \\cdots + b _ {k-1, 1} x +b _ {k-1, 0} \\right) \\\\\r\n& = \\cdots +( b _ {k-1, n} +b _ {k-1, n-1} ) x^n + \\cdots +( b _ {k-1, 1} +b _ {k-1, 0} ) x +b _ {k-1, 0}\r\n\\end{align}\\]\r\n\u6761\u4ef6\u3088\u308a\r\n\\[\r\nb _ {k,n} = b _ {k-1,n} +b _ {k-1,n-1} , \\cdots , b _ {k,1} = b _ {k-1,1}+b _ {k-1,0} , \\ b _ {k,0} = b _ {k-1,0}\r\n\\]\r\n\u306f\u3059\u3079\u3066\u6574\u6570\u306a\u306e\u3067, \\(b _ {k-1,0} , b _ {k-1,1} , \\cdots , b _ {k-1,n}\\) \u3082\u3059\u3079\u3066\u6574\u6570\u3067\u3042\u308b.<br \/>\r\n\u3053\u308c\u3092\u7e70\u8fd4\u3057\u7528\u3044\u308c\u3070, \\(b _ {0,0} , b _ {0,1} , \\cdots , b _ {0,n}\\) \u3059\u306a\u308f\u3061 \\(a _ 0 , a _ 1 , \\cdots , a _ n\\) \u306f\u3059\u3079\u3066\u6574\u6570\u3067\u3042\u308b.<br \/>\r\n\u3088\u3063\u3066, \u984c\u610f\u306f\u793a\u3055\u308c\u305f.<\/p>\r\n","protected":false},"excerpt":{"rendered":"\\(n\\) \u3068 \\(k\\) \u3092\u6b63\u306e\u6574\u6570\u3068\u3057, \\(P(x)\\) \u3092\u6b21\u6570\u304c \\(n\\) \u4ee5\u4e0a\u306e\u6574\u5f0f\u3068\u3059\u308b. \u6574\u5f0f \\((1+x)^k P(x)\\) \u306e \\(n\\) \u6b21\u4ee5\u4e0b\u306e\u9805\u306e\u4fc2\u6570\u304c\u3059\u3079\u3066\u6574\u6570\u306a\u3089\u3070, \\(P(x)\\) \u306e &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/tkr200701\/\">\u7d9a\u304d\u3092\u8aad\u3080 <span class=\"meta-nav\">&rarr;<\/span><\/a>","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[85],"tags":[139,109],"class_list":["post-597","post","type-post","status-publish","format-standard","hentry","category-tokyo_r_2007","tag-tokyo_r","tag-109"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/597","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/comments?post=597"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/597\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=597"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=597"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=597"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}