{"id":5327,"date":"2026-02-16T10:00:23","date_gmt":"2026-02-16T01:00:23","guid":{"rendered":"https:\/\/winroadrikeijyuku.com\/oita\/?p=5327"},"modified":"2026-02-12T20:46:11","modified_gmt":"2026-02-12T11:46:11","slug":"%e9%83%a8%e5%88%86%e7%a9%8d%e5%88%86-2024-%e4%b9%9d%e5%b7%9e%e5%a4%a7-%e5%a4%a7%e5%88%86%e5%b8%82-%e5%a4%a7%e5%ad%a6%e5%8f%97%e9%a8%93-%e6%95%b0%e5%ad%a6-%e5%a1%be-%e5%a4%a7%e5%88%86%e7%90%86","status":"publish","type":"post","link":"https:\/\/winroadrikeijyuku.com\/oita\/2026\/02\/16\/%e9%83%a8%e5%88%86%e7%a9%8d%e5%88%86-2024-%e4%b9%9d%e5%b7%9e%e5%a4%a7-%e5%a4%a7%e5%88%86%e5%b8%82-%e5%a4%a7%e5%ad%a6%e5%8f%97%e9%a8%93-%e6%95%b0%e5%ad%a6-%e5%a1%be-%e5%a4%a7%e5%88%86%e7%90%86\/","title":{"rendered":"\u90e8\u5206\u7a4d\u5206( 2024 \u4e5d\u5dde\u5927) | \u5927\u5206\u5e02 \u5927\u5b66\u53d7\u9a13 \u6570\u5b66 \u587e | \u5927\u5206\u7406\u7cfb\u5c02\u9580\u587eWINROAD"},"content":{"rendered":"

\u554f\u984c<\/p>\n

\u81ea\u7136\u6570m\u3001n\u306b\u5bfe\u3057\u3066<\/p>\n

\u200b\\( I(m,n)=\\displaystyle\\int_1^ex^me^x(\\log x)^ndx \\)<\/span>\u200b\u3068\u3059\u308b\u3002\u4ee5\u4e0b\u306e\u554f\u3044\u306b\u7b54\u3048\u3088\u3002<\/p>\n

(1) \u200b\\( I(m+1,n+1) \\)<\/span>\u200b\u3092\u200b\\( I(m,n+1),\\ I(m,n),\\ m,\\ n \\)<\/span>\u200b\u3092\u7528\u3044\u3066\u8868\u305b\u3002<\/p>\n

(2)\u3059\u3079\u3066\u306e\u81ea\u7136\u6570m\u306b\u5bfe\u3057\u3066\u3001\u200b\\( \\displaystyle \\lim_{n \\to\\infty}I(m,n)=0 \\)<\/span>\u200b\u304c\u6210\u308a\u7acb\u3064\u3053\u3068\u3092\u793a\u305b\u3002<\/p>\n

\n

(1) \u200b\\( \\small{I(m+1,n+1)=\\displaystyle\\int_1^ex^{m+1}e^x(log x)^{n+1}dx\\\\=\\displaystyle\\int_1^e(e^x)’x^{m+1}(log x)^{n+1}dx\\\\=\\bigl \\lfloor e^xx^{m+1}(\\log x)^{n+1}\\bigl \\rfloor_1^e-\\displaystyle\\int_1^ee^x\\{x^{m+1}(log x)^{n+1}\\}’dx }\\)<\/span>\u200b<\/span><\/p>\n

\\(\\small{=e^{e+m+1}-\\displaystyle\\int_1^ee^x\\{(m+1)x^{m}(log x)^{n+1}+x^{m+1}(n+1)(\\log x)^n\\dfrac{1}{x}\\}dx}\\)<\/span><\/span><\/p>\n

\u200b\\( \\small{=e^{e+m+1}-\\displaystyle(m+1)\\int_1^ee^xx^{m}(log x)^{n+1}dx-\\displaystyle(n+1)\\int_1^ee^xx^{m}(log x)^{n}\\\\ =e^{e+m+1}-(m+1)I(m.n+1)-(n+1)I(m,n)} \\)<\/span>\u200b<\/span><\/p>\n

\n

(2) \u200b\\( 1\\leqq x\\leqq e \\)<\/span>\u200b\u306b\u304a\u3044\u3066\u200b\\( x^me^x(\\log x)^n\\geqq0 \\)<\/span>\u200b<\/span><\/p>\n

\u3088\u3063\u3066\u200b\\( I(m,n)=\\displaystyle\\int_1^ex^me^x(\\log x)^ndx\\geqq0 \\)<\/span>\u200b<\/span><\/p>\n

\u200b\\( I(m+1,n+1)=\\displaystyle\\int_1^ex^{m+1}e^x(log x)^{n+1}dx\\geqq0 \\)<\/span>\u200b<\/span><\/p>\n

\u200b\\( I(m,n+1)=\\displaystyle\\int_1^ee^xx^{m}(log x)^{n+1}dx\\geqq0 \\)<\/span>\u200b<\/span><\/p>\n

(1)\u3088\u308a<\/span><\/p>\n

\u200b\\( 0\\leqq I(m,n)=\\dfrac{e^{e+m+1}}{n+1}-\\dfrac{1}{n+1}(m+1)I(m,n+1)-\\dfrac{1}{n+1}I(m+1,n+1)\\leqq \\dfrac{e^{e+m+1}}{n+1} \\)<\/span>\u200b<\/span><\/p>\n

\u200b\\( \\displaystyle \\lim_{n \\to\\infty}\\dfrac{e^{e+m+1}}{n+1}=0\u00a0 \\)<\/span>\u200b<\/span><\/p>\n

\u306f\u3055\u307f\u3046\u3061\u306e\u539f\u7406\u3088\u308a\u3002<\/span><\/p>\n

\u200b\\( \\displaystyle \\lim_{n \\to\\infty}I(m,n)=0 \\)<\/span>\u200b<\/span><\/p>\n

 <\/p>\n

\uff08\u5927\u5206\u7406\u7cfb\u5c02\u9580\u587eWINROAD <\/span>\u9996\u85e4\uff09<\/span><\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

\u554f\u984c \u81ea\u7136\u6570m\u3001n\u306b\u5bfe\u3057\u3066 \u200b\\( I(m,n)=\\displaystyle\\int_1^ex^me^x(\\log x)^ndx \\)\u200b\u3068\u3059\u308b\u3002\u4ee5\u4e0b\u306e\u554f\u3044\u306b\u7b54\u3048\u3088\u3002 (1) \u200b\\( I(m+1,n+1) \\)\u200b\u3092\u200b\\( <\/p>\n

\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"vkexunit_cta_each_option":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-5327","post","type-post","status-publish","format-standard","hentry","category-1"],"_links":{"self":[{"href":"https:\/\/winroadrikeijyuku.com\/oita\/wp-json\/wp\/v2\/posts\/5327","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/winroadrikeijyuku.com\/oita\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/winroadrikeijyuku.com\/oita\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/winroadrikeijyuku.com\/oita\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/winroadrikeijyuku.com\/oita\/wp-json\/wp\/v2\/comments?post=5327"}],"version-history":[{"count":27,"href":"https:\/\/winroadrikeijyuku.com\/oita\/wp-json\/wp\/v2\/posts\/5327\/revisions"}],"predecessor-version":[{"id":5354,"href":"https:\/\/winroadrikeijyuku.com\/oita\/wp-json\/wp\/v2\/posts\/5327\/revisions\/5354"}],"wp:attachment":[{"href":"https:\/\/winroadrikeijyuku.com\/oita\/wp-json\/wp\/v2\/media?parent=5327"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/winroadrikeijyuku.com\/oita\/wp-json\/wp\/v2\/categories?post=5327"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/winroadrikeijyuku.com\/oita\/wp-json\/wp\/v2\/tags?post=5327"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}