\u62c9\u666e\u62c9\u65af\u53ef\u4ece\u5e42\u7ea7\u6570\u63a8\u5012\u51fa\u6765(n=0,1,2,3........)
\n$$
\n\\sum _ { 0 } ^ { \\infty } a _ { n } x ^ { n } = A ( x )
\n$$
\n\u6211\u4eec\u7528\u79bb\u6563\u51fd\u6570$$ a(n) $$\u628a$$ a _ { n } $$ \u66ff\u6362\u6389
\n$$
\n\\sum _ { 0 } ^ { \\infty } a(n) x ^ { n } = A ( x )
\n$$
\n\u4f8b\u5982\u5f53$$a(n)=1$$ ,$$ a(n) =\\frac { 1 } { n ! } $$\u7684\u65f6\u5019,$$ A(x) $$\u5206\u522b\u7b49\u4e8e
\n$$
\n\\begin{array} { l } { a ( n ) \\rightarrow A ( x ) } \ { 1 \\rightarrow \\frac { 1 } { 1 - x } \\quad | x | < 1 } \ { \\frac { 1 } { n ! } \\rightarrow e ^ { x } } \\end{array}
\n$$<\/p>\n
\u6211\u4eec\u7528\u65f6\u95f4t(0<=t<=\u221e)\u4ee3\u66ff\u81ea\u7136\u6570n(n=0,1,2,3......)
\n$$
\n\\int _ { 0 } ^ { \\infty } a(t) x ^ { t } = A ( x )
\n$$
\n\u6211\u4eec\u505a\u5fae\u79ef\u5206\u7684\u65f6\u5019\u901a\u5e38\u4e0d\u559c\u6b22\u5e95\u6570\u662f\u4e2ax,\u6211\u4eec\u5e0c\u671b\u5e95\u6570\u662fe
\n$$
\nx = e ^ { \\ln x }
\n$$
\n\u6211\u4eec\u5e0c\u671b,$$ A(x) $$\u662f\u6536\u655b\u7684\uff0c\u6240\u4ee5x<1,<\/p>\n
\u5982\u4f55x<0,\u5982x=-1,\u90a3\u4e480<t<1\u662f$$x ^ { t }$$\u5c31\u53d8\u6210\u865a\u6570\u4e86\uff0c\u8fd9\u4e2a\u4e5f\u4e0d\u662f\u6211\u4eec\u8981\u7684\uff0c\u6240\u4ee50<x,<\/p>\n
\u6240\u4ee50<x<1,<\/p>\n
\u6240\u4ee5$$\\ln x<0$$.<\/p>\n
\u6211\u4eec\u7528\u6b63\u6570s\u4ee3\u66ff\u8d1f\u6570 $$ \\ln x$$,\u5373$$ s=-\\ln x$$<\/p>\n
\u7531\u6b64\uff0c\u62c9\u666e\u62c9\u65af\u53d8\u6362\u5df2\u7ecf\u6210\u578b\uff0c
\n$$
\n\\int _ { 0 } ^ { a } a ( t ) e ^ { - s t } d t = A \\left( e ^ { - s } \\right) = A ( s )
\n$$
\n$$A \\left( e ^ { - s } \\right)$$\uff0c\u662f\u5173\u4e8es\u7684\u7b80\u5355\u51fd\u6570\uff0c\u56e0\u6b64\u76f4\u63a5\u5199\u4e3a$$A ( s )$$
\n\u62c9\u666e\u62c9\u65af\u53d8\u5316\u6700\u91cd\u8981\u7684\u7279\u6027\u662f\u628a\u5173\u4e8e\u4e00\u4e2a\u53d8\u91cf\u7684\u51fd\u6570\u8f6c\u5316\u4e3a\u4e86\u5173\u4e8e\u53e6\u4e00\u4e2a\u53d8\u91cf\u7684\u51fd\u6570\uff0c\u8fd9\u4e2a\u5f88\u6709\u610f\u4e49<\/p>\n","protected":false},"excerpt":{"rendered":"
\u79bb\u6563 \u62c9\u666e\u62c9\u65af\u53ef\u4ece\u5e42\u7ea7\u6570\u63a8\u5012\u51fa\u6765(n=0,1,2,3……..) $$ \\sum _ { 0 } ^ { \\infty } ","protected":false},"author":1,"featured_media":170,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3,11],"tags":[],"_links":{"self":[{"href":"https:\/\/www.sanburs.xyz\/index.php\/wp-json\/wp\/v2\/posts\/154"}],"collection":[{"href":"https:\/\/www.sanburs.xyz\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.sanburs.xyz\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.sanburs.xyz\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.sanburs.xyz\/index.php\/wp-json\/wp\/v2\/comments?post=154"}],"version-history":[{"count":5,"href":"https:\/\/www.sanburs.xyz\/index.php\/wp-json\/wp\/v2\/posts\/154\/revisions"}],"predecessor-version":[{"id":158,"href":"https:\/\/www.sanburs.xyz\/index.php\/wp-json\/wp\/v2\/posts\/154\/revisions\/158"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.sanburs.xyz\/index.php\/wp-json\/wp\/v2\/media\/170"}],"wp:attachment":[{"href":"https:\/\/www.sanburs.xyz\/index.php\/wp-json\/wp\/v2\/media?parent=154"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.sanburs.xyz\/index.php\/wp-json\/wp\/v2\/categories?post=154"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.sanburs.xyz\/index.php\/wp-json\/wp\/v2\/tags?post=154"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}