{"id":1646,"date":"2023-05-10T18:05:41","date_gmt":"2023-05-10T10:05:41","guid":{"rendered":"http:\/\/zhang.mba\/?p=1646"},"modified":"2023-05-10T18:11:25","modified_gmt":"2023-05-10T10:11:25","slug":"mi-ji-shu-de-he-han-shu","status":"publish","type":"post","link":"https:\/\/zhang.mba\/index.php\/2023\/05\/10\/18\/05\/41\/1646\/mi-ji-shu-de-he-han-shu\/%e9%ab%98%e7%ad%89%e6%95%b0%e5%ad%a6\/zhangzhiqi\/","title":{"rendered":"\u5e42\u7ea7\u6570\u7684\u548c\u51fd\u6570"},"content":{"rendered":"<p>\u5e42\u7ea7\u6570\u7684\u548c\u51fd\u6570\u4e5f\u88ab\u79f0\u4e3a\u5e42\u51fd\u6570\uff0c\u662f\u6307\u5e42\u7ea7\u6570\u5728\u6536\u655b\u57df\u5185\u7684\u548c\u3002\u5177\u4f53\u5730\uff0c\u5bf9\u4e8e\u5e42\u7ea7\u6570\uff1a<\/p>\n<p>$$<br \/>\n\\sum_{n=0}^\\infty a_n x^n = a_0 + a_1 x + a_2 x^2 + \\cdots + a_n x^n + \\cdots<br \/>\n$$<\/p>\n<p>\u8bbe $R$ \u662f\u8be5\u5e42\u7ea7\u6570\u7684\u6536\u655b\u534a\u5f84\uff0c\u5219\u5f53 $|x| < R$ \u65f6\uff0c\u5e42\u7ea7\u6570\u7edd\u5bf9\u6536\u655b\uff0c\u56e0\u6b64\u53ef\u4ee5\u5b9a\u4e49\u5e42\u51fd\u6570\uff1a\n\n$$\nf(x) = \\sum_{n=0}^\\infty a_n x^n\n$$\n\n$f(x)$ \u5c31\u662f\u8be5\u5e42\u7ea7\u6570\u7684\u548c\u51fd\u6570\uff0c\u5b83\u7684\u5b9a\u4e49\u57df\u662f $(-R, R)$\u3002\n\n\u5e42\u51fd\u6570\u5177\u6709\u826f\u597d\u7684\u6027\u8d28\uff0c\u5305\u62ec\uff1a\n\n1. \u5e42\u51fd\u6570\u5728\u6536\u655b\u57df\u5185\u8fde\u7eed\u3002\n\n2. \u5e42\u51fd\u6570\u7684\u5bfc\u6570\u53ef\u4ee5\u901a\u8fc7\u9010\u9879\u6c42\u5bfc\u5f97\u5230\uff1a\n\n$$\nf'(x) = \\sum_{n=1}^\\infty na_n x^{n-1}\n$$\n\n3. \u5e42\u51fd\u6570\u7684\u4e0d\u5b9a\u79ef\u5206\u53ef\u4ee5\u901a\u8fc7\u9010\u9879\u79ef\u5206\u5f97\u5230\uff1a\n\n$$\n\\int f(x) dx = \\sum_{n=0}^\\infty \\frac{a_n}{n+1}x^{n+1} + C\n$$\n\n\u5176\u4e2d $C$ \u662f\u79ef\u5206\u5e38\u6570\u3002\n\n\u5e42\u51fd\u6570\u5728\u5fae\u79ef\u5206\u3001\u5e38\u5fae\u5206\u65b9\u7a0b\u7b49\u9886\u57df\u4e2d\u5177\u6709\u91cd\u8981\u7684\u5e94\u7528\u3002\u4f8b\u5982\uff0c\u53ef\u4ee5\u901a\u8fc7\u5e42\u51fd\u6570\u7684\u6027\u8d28\u6765\u6c42\u89e3\u67d0\u4e9b\u5fae\u5206\u65b9\u7a0b\u7684\u521d\u503c\u95ee\u9898\u3002\n<\/p>\n<!--CusAds0-->\n<div style=\"font-size: 0px; height: 0px; line-height: 0px; margin: 0; padding: 0; clear: both;\"><\/div>","protected":false},"excerpt":{"rendered":"<p>\u5e42\u7ea7\u6570\u7684\u548c\u51fd\u6570\u4e5f\u88ab\u79f0\u4e3a\u5e42\u51fd\u6570\uff0c\u662f\u6307\u5e42\u7ea7\u6570\u5728\u6536\u655b\u57df\u5185\u7684\u548c\u3002\u5177\u4f53\u5730\uff0c\u5bf9\u4e8e\u5e42\u7ea7\u6570\uff1a $$ \\sum_{n=0}^\\infty a_n x^n = a_0 + a_1 x + a_2 x^2 + \\cdots + a_n x^n + \\cdots $$ \u8bbe $R$ \u662f\u8be5\u5e42\u7ea7\u6570\u7684\u6536\u655b\u534a\u5f84\uff0c\u5219\u5f53 $|x| < R$ \u65f6\uff0c\u5e42\u7ea7\u6570\u7edd\u5bf9\u6536\u655b\uff0c\u56e0\u6b64\u53ef\u4ee5 ...\n<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_bbp_topic_count":0,"_bbp_reply_count":0,"_bbp_total_topic_count":0,"_bbp_total_reply_count":0,"_bbp_voice_count":0,"_bbp_anonymous_reply_count":0,"_bbp_topic_count_hidden":0,"_bbp_reply_count_hidden":0,"_bbp_forum_subforum_count":0},"categories":[20],"tags":[59],"_links":{"self":[{"href":"https:\/\/zhang.mba\/index.php\/wp-json\/wp\/v2\/posts\/1646"}],"collection":[{"href":"https:\/\/zhang.mba\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/zhang.mba\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/zhang.mba\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/zhang.mba\/index.php\/wp-json\/wp\/v2\/comments?post=1646"}],"version-history":[{"count":0,"href":"https:\/\/zhang.mba\/index.php\/wp-json\/wp\/v2\/posts\/1646\/revisions"}],"wp:attachment":[{"href":"https:\/\/zhang.mba\/index.php\/wp-json\/wp\/v2\/media?parent=1646"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/zhang.mba\/index.php\/wp-json\/wp\/v2\/categories?post=1646"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/zhang.mba\/index.php\/wp-json\/wp\/v2\/tags?post=1646"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}