{"id":157,"date":"2024-01-04T11:41:51","date_gmt":"2024-01-04T03:41:51","guid":{"rendered":"https:\/\/big-tan.top\/?p=157"},"modified":"2024-02-14T09:29:02","modified_gmt":"2024-02-14T01:29:02","slug":"%e6%ac%a7%e6%8b%89%e7%a5%9e%e4%bd%9c-%e8%ae%a9%e4%bb%96%e5%90%8d%e6%89%ac%e5%a4%a9%e4%b8%8b%e7%9a%84%e5%b7%b4%e5%a1%9e%e5%b0%94%e9%97%ae%e9%a2%98","status":"publish","type":"post","link":"https:\/\/big-tan.top\/?p=157","title":{"rendered":"\u6b27\u62c9\u795e\u4f5c&#8212;-\u8ba9\u4ed6\u540d\u626c\u5929\u4e0b\u7684\u201c\u5df4\u585e\u5c14\u95ee\u9898\u201d"},"content":{"rendered":"\n<div class=\"wp-block-stackable-columns stk-block-columns stk-block stk-ecae445 stk-block-background\" data-block-id=\"ecae445\"><style>.stk-ecae445{background-color:#ffe2c7 !important;border-top-left-radius:18px !important;border-top-right-radius:18px !important;border-bottom-right-radius:18px !important;border-bottom-left-radius:18px !important;overflow:hidden !important;border-style:solid !important;margin-bottom:23px !important}.stk-ecae445:before{background-color:#ffe2c7 !important}<\/style><div class=\"stk-row stk-inner-blocks stk-block-content stk-content-align stk-ecae445-column\">\n<div class=\"wp-block-stackable-column stk-block-column stk-column stk-block stk-4b0a9ed\" data-v=\"4\" data-block-id=\"4b0a9ed\"><div class=\"stk-column-wrapper stk-block-column__content stk-container stk-4b0a9ed-container stk--no-background stk--no-padding\"><div class=\"stk-block-content stk-inner-blocks stk-4b0a9ed-inner-blocks\">\n<div class=\"wp-block-stackable-text stk-block-text stk-block stk-2d50e96\" data-block-id=\"2d50e96\"><p class=\"stk-block-text__text\">\u2003\u20031644\u5e74\u745e\u58eb\u6570\u5b66\u5bb6\u76ae\u8036\u7279\u7f57\u00b7\u95e8\u6208\u5229\u63d0\u51fa\u4e86\u4e00\u4e2a\u95ee\u9898\uff0c\u6240\u6709\u81ea\u7136\u6570\u5012\u6570\u7684\u5e73\u65b9\u548c\u662f\u591a\u5c11\uff1f\u8fd9\u5c31\u662f\u6570\u5b66\u5386\u53f2\u4e0a\u8457\u540d\u7684\u201c\u5df4\u585e\u5c14\u95ee\u9898\u201d\uff0c\u8fd9\u4e2a\u770b\u4f3c\u7b80\u5355\u7684\u95ee\u9898\u56f0\u6270\u4e86\u6570\u5b66\u5bb6\u4eec\u4e00\u4e2a\u591a\u4e16\u7eaa\uff01<\/p><\/div>\n<\/div><\/div><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-stackable-columns stk-block-columns stk-block stk-a7adbfd stk-block-background\" data-block-id=\"a7adbfd\"><style>.stk-a7adbfd{border-top-left-radius:18px !important;border-top-right-radius:18px !important;border-bottom-right-radius:18px !important;border-bottom-left-radius:18px !important;overflow:hidden !important;border-style:solid !important}<\/style><div class=\"stk-row stk-inner-blocks stk-block-content stk-content-align stk-a7adbfd-column\">\n<div class=\"wp-block-stackable-column stk-block-column stk-column stk-block stk-4246c59\" data-v=\"4\" data-block-id=\"4246c59\"><div class=\"stk-column-wrapper stk-block-column__content stk-container stk-4246c59-container stk--no-background stk--no-padding\"><div class=\"stk-block-content stk-inner-blocks stk-4246c59-inner-blocks\">\n<div class=\"wp-block-stackable-text stk-block-text stk-block stk-efc0358\" data-block-id=\"efc0358\"><style>.stk-efc0358 .stk-block-text__text{color:#ff6900 !important}<\/style><p class=\"stk-block-text__text has-text-color\">\u2003\u2003<strong>$\\displaystyle\\sum_{n=1}^\\infty \\frac1{n^2}= \\frac1{1^2}+\\frac1{2^2}+\\frac1{3^2}+\\frac1{4^2}+\\dots=?$<\/strong><\/p><\/div>\n<\/div><\/div><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-stackable-columns stk-block-columns stk-block stk-4a3fa04 stk-block-background\" data-block-id=\"4a3fa04\"><style>.stk-4a3fa04{background-color:#ffe2c7 !important;border-top-left-radius:18px !important;border-top-right-radius:18px !important;border-bottom-right-radius:18px !important;border-bottom-left-radius:18px !important;border-style:solid !important;overflow:auto !important}.stk-4a3fa04:before{background-color:#ffe2c7 !important}<\/style><div class=\"stk-row stk-inner-blocks stk-block-content stk-content-align stk-4a3fa04-column\">\n<div class=\"wp-block-stackable-column stk-block-column stk-column stk-block stk-fb96aaa\" data-v=\"4\" data-block-id=\"fb96aaa\"><div class=\"stk-column-wrapper stk-block-column__content stk-container stk-fb96aaa-container stk--no-background stk--no-padding\"><div class=\"stk-block-content stk-inner-blocks stk-fb96aaa-inner-blocks\">\n<div class=\"wp-block-stackable-text stk-block-text stk-block stk-ecc0701\" data-block-id=\"ecc0701\"><p class=\"stk-block-text__text\">\u2003\u2003\u770b\u8d77\u6765\u597d\u50cf\u4e0d\u7b97\u662f\u4e00\u4e2a\u7279\u522b\u56f0\u96be\u7684\u95ee\u9898\uff0c\u4f46\u662f\u5f88\u4e45\u4ee5\u6765\uff0c\u90fd\u6ca1\u6709\u4eba\u80fd\u591f\u7ed9\u51fa\u7b54\u6848\u6765\u3002\u8fd9\u4e2a\u95ee\u9898\u96be\u5012\u4e86\u5f88\u591a\u8457\u540d\u6570\u5b66\u5bb6\uff0c\u6bd4\u5982\u4e24\u4f4d\u5fae\u79ef\u5206\u7684\u521b\u59cb\u4eba\uff0c\u725b\u987f\u548c\u83b1\u5e03\u5c3c\u8328\u3002\u83b1\u5e03\u5c3c\u8328\u53d1\u73b0\u4e86\u7b2c\u4e00\u4e2a\u8ba1\u7b97\u03c0\u7684\u65e0\u7a77\u7ea7\u6570\u5f62\u5f0f\u3002<br>\u2003\u2003$\\displaystyle\\frac\\pi4=\\frac11-\\frac13+\\frac15-\\frac17+\\frac19-\\frac1{11}+\\dots$<br>\u2003\u2003\u8fd9\u662f\u4e00\u4e2a\u524d\u6240\u672a\u89c1\u7684\u6c42\u5706\u5468\u7387\u7684\u8868\u8fbe\u5f0f\uff0c\u4e8e\u662f\u83b1\u5e03\u5c3c\u8328\u5c31\u81ea\u8be9\uff0c\u7ed9\u51fa\u4efb\u4f55\u65e0\u7a77\u7ea7\u6570\u6765\uff0c\u4ed6\u90fd\u53ef\u4ee5\u6c42\u51fa\u6765\u548c\u3002\u6211\u4eec\u5c31\u5047\u5b9a\u5728\u5f53\u65f6\u4ed6\u7684\u786e\u6709\u8bf4\u8fd9\u756a\u72c2\u8a00\u7684\u5b9e\u529b\uff0c\u4f46\u662f\u4ed6\u7684\u786e\u5728\u5df4\u585e\u5c14\u95ee\u9898\u4e0a\u7ffb\u4e86\u8239\uff0c\u76f4\u5230\u6b7b\u4e5f\u6ca1\u770b\u5230\u8fd9\u4e2a\u95ee\u9898\u7684\u6700\u7ec8\u7b54\u6848\u3002<br>\u2003\u2003\u957f\u4e45\u4ee5\u6765\uff0c\u8fd9\u90fd\u662f\u6570\u5b66\u754c\u4e00\u4e2a\u60ac\u800c\u672a\u51b3\u7684\u95ee\u9898\uff0c\u76f4\u5230100\u591a\u5e74\u4e4b\u540e\u7684\u6b27\u62c9\u5927\u795e\u51fa\u624b\u89e3\u51b3\uff0c\u5df4\u585e\u5c14\u95ee\u9898\u56e0\u6b64\u5f97\u540d\uff0c\u5df4\u585e\u5c14\u662f\u6b27\u62c9\u548c\u4f2f\u52aa\u5229\u5bb6\u65cf\u7684\u6545\u4e61\u3002<br>\u2003\u2003\u4e0b\u9762\u770b\u770b\u6b27\u62c9\u5bf9\u4e8e\u5df4\u585e\u5c14\u7ea7\u6570\u95ee\u9898\u7684\u6c42\u89e3\u8fc7\u7a0b\u3002<br>$\\begin{split}&amp;\\sum_{n=1}^\\infty \\frac1{n^2}= \\frac1{1^2}+\\frac1{2^2}+\\frac1{3^2}+\\frac1{4^2}+\\dots=? \\\\ &amp;\u7531\u6cf0\u52d2\u5c55\u5f00\u5f0f\u5f97\u5230\uff1asinx= x-\\frac{x^3}{3!}+\\frac{x^5}{5!}-\\frac{x^7}{7!}+\\dots+{(-1)^{m-1}}\\frac{x^{2m-1}}{(2m-1)!}  \\quad (1) \\\\&amp;\u6784\u9020\u51fd\u6570f(x)=\\frac{sinx}{x}=1-\\frac{x^2}{3!}+\\frac{x^4}{5!}-\\frac{x^6}{7!}+\\dots+{(-1)^{m-1}}\\frac{x^{2m-2}}{(2m-1)!}\\quad (2) \\\\ &amp;f(x)\u7684\u5168\u90e8\u96f6\u70b9\uff0cx=\\pm n\\pi \uff0cn=1,2,3,\\dots \\\\ &amp;\u5f97\u5230f(x)=(1-\\frac x\\pi)(1+\\frac x\\pi) (1-\\frac x{2\\pi})(1+\\frac x{2\\pi})(1-\\frac x{3\\pi})(1+\\frac x{3\\pi}) \\dots(1-\\frac x{n\\pi})(1+\\frac x{n\\pi}) \\quad (3)\\\\ &amp;\u5373f(x)=(1-\\frac{x^2}{\\pi^2} )(1-\\frac{x^2}{4\\pi^2})(1-\\frac{x^2}{9\\pi^2}) \\dots(1-\\frac{x^2}{n^2\\pi^2})=1-\\frac{x^2}{3!}+\\frac{x^4}{5!}-\\frac{x^6}{7!}+\\dots+{(-1)^{m-1}}\\frac{x^{2m-2}}{(2m-1)!}\\quad (4) \\\\&amp;\u6bd4\u8f83(4)\u5f0f\u4e24\u8fb9 x^2\u9879\u7684\u7cfb\u6570\uff0c\u53ef\u4ee5\u5f97\u5230\uff1a\\\\&amp;-(\\frac1{\\pi^2}+\\frac1{4\\pi^2}+\\frac1{9\\pi^2}+\\frac1{16\\pi^2}+\\dots+\\frac1{n^2\\pi^2})=-\\frac1{3!}\\qquad (5)\\\\&amp;\u6240\u4ee5\uff1a\\displaystyle\\sum_{n=1}^\\infty \\frac1{n^2}= \\frac1{1^2}+\\frac1{2^2}+\\frac1{3^2}+\\frac1{4^2}+\\dots=\\frac{\\pi^2}6\\end{split}$<br>\u2003\u2003\u8fd9\u91cc\u6b27\u62c9\u901a\u8fc7\u6784\u9020\u4e86\u4e00\u4e2a\u7279\u6b8a\u51fd\u6570\uff0c\u5e76\u6700\u7ec8\u7531\u8fd9\u4e2a\u51fd\u6570\u7684\u6cf0\u52d2\u5c55\u5f00\u5f0f\u5f97\u5230\u4e86\u6b63\u786e\u7684\u7ed3\u8bba\u3002<br>\u2003\u2003\u8fd9\u4e2a\u7ea7\u6570\u7684\u6536\u655b\u6027\u5f88\u597d\u8bc1\u660e\uff0c\u6b27\u62c9\u7684\u795e\u6765\u4e4b\u7b14\u5728(2),(3)\u4e4b\u95f4\u7684\u8f6c\u6362\uff0c\u7531\u4e8e\u8fd9\u4e2a\u51fd\u6570f(x)\u5bb9\u6613\u770b\u51fa\u6765\u5168\u90e8\u7684\u96f6\u70b9\uff0c\u6b27\u62c9\u521b\u9020\u6027\u5730\u628a\u7528\u5728\u6709\u9650\u591a\u9879\u5f0f\u7684\u56e0\u5f0f\u4e58\u79ef\u5f62\u5f0f\u7528\u5728\u4e86\u65e0\u9650\u9879\u591a\u9879\u5f0f\u4e2d\u3002\u4e3a\u4ec0\u4e48\u6b27\u62c9\u8981\u5c06(3)\u5f0f\u5199\u6210\u8fd9\u6837\u7684\u8fde\u4e58\u5f62\u5f0f\uff0c\u800c\u4e0d\u662f\u522b\u7684\u5f62\u5f0f\uff1f\u8fd9\u662f\u56e0\u4e3af(x)\u7684\u6cf0\u52d2\u5c55\u5f00\u5f0f\u53f3\u8fb9\u6709\u4e00\u4e2a\u5e38\u65701\uff0c\u6240\u4ee5\u7b49\u5f0f\u5de6\u8fb9\u5c55\u5f00\u540e\u4e5f\u5e94\u8be5\u51fa\u73b0\u6709\u4e2a1\u4e0e\u4e4b\u5bf9\u5e94\u3002<br>\u2003\u2003\u5176\u5b9e(2),(3)\u4e4b\u95f4\u7684\u8df3\u8f6c\u5f88\u6709\u98ce\u9669\uff0c\u5f88\u591a\u65f6\u5019\u5bf9\u4e8e\u6709\u9650\u9879\u663e\u800c\u6613\u89c1\u7684\u5904\u7406\u65b9\u6cd5\u653e\u5728\u65e0\u7a77\u591a\u9879\u91cc\u5374\u5b8c\u5168\u662f\u9519\u8bef\u7684\u3002\u6b27\u62c9\u5f53\u7136\u77e5\u9053\u8fd9\u4e48\u505a\u7684\u5192\u9669\uff0c\u4f46\u662f\u6b27\u62c9\u662f\u4e00\u4f4d\u4e3e\u4e16\u65e0\u53cc\u7684\u8ba1\u7b97\u5927\u5e08\uff0c\u4ed6\u8ba1\u7b97\u51fa\u5df4\u585e\u5c14\u7ea7\u6570\u7684\u6570\u503c\u5927\u7ea6\u57281.645\u5de6\u53f3\uff0c\u8ddf\u4ed6\u5f97\u5230\u7684\u7ed3\u679c$\\displaystyle\\frac{\\pi^2}{6}$\u5b8c\u5168\u4e00\u6837\uff0c\u66f4\u52a0\u575a\u4fe1\u5f97\u5230\u7684\u7ed3\u679c\u662f\u6b63\u786e\u65e0\u8bef\u7684\u3002\u4e8b\u5b9e\u4e0a\uff0c\u5df4\u585e\u5c14\u7ea7\u6570\u6536\u655b\u7684\u901f\u5ea6\u6781\u6162\uff0c\u5927\u7ea6\u8981\u8ba1\u7b97\u5230\u7b2c10000\u9879\u624d\u80fd\u7cbe\u786e\u5230\u5c0f\u6570\u70b9\u540e\u4e09\u4f4d\uff01<br>\u2003\u20031735\u5e74\uff0c\u6b27\u62c9\u5927\u80c6\u5730\u628a\u8fd9\u4e2a\u7ed3\u8bba\u53d1\u8868\u51fa\u6765\uff0c\u8f70\u52a8\u4e86\u6574\u4e2a\u6570\u5b66\u754c\uff0c\u5e74\u4ec528\u5c81\u7684\u6b27\u62c9\u89e3\u51b3\u4e86\uff0c\u83b1\u5e03\u5c3c\u8328\uff0c\u725b\u987f\u4e5f\u4e0d\u66fe\u89e3\u51b3\u7684\u96be\u9898\uff0c\u4ece\u6b64\u540d\u626c\u5929\u4e0b\u30026\u5e74\u4e4b\u540e\u76841741\u5e74\uff0c\u6b27\u62c9\u7ec8\u4e8e\u628a\u8fd9\u4e2a\u7455\u75b5\u4e5f\u8865\u4e0a\u4e86\uff0c\u6b64\u65f6\u5df4\u585e\u5c14\u95ee\u9898\u624d\u7b97\u771f\u6b63\u88ab\u5b8c\u5168\u89e3\u51b3\u3002<br>\u2003\u2003\u5982\u679c\u5c55\u5f00(3)\u5f0f\u5de6\u8fb9\uff0c\u6211\u4eec\u53d1\u73b0\u5de6\u53f3\u4e24\u8fb9\u53ea\u6709x\u7684\u5076\u6570\u6b21\u9879\uff0c\u800c\u4e0d\u4f1a\u51fa\u73b0\u4efb\u4f55x\u7684\u5947\u6570\u6b21\u9879\u3002\u5047\u5982\uff0c\u6211\u4eec\u6709\u529e\u6cd5\u628a(3)\u5f0f\u5de6\u8fb9\u5173\u4e8ex\u7684\u6240\u6709\u7cfb\u6570\u90fd\u8ba1\u7b97\u51fa\u6765\uff0c\u7406\u8bba\u4e0a\u6211\u4eec\u5c31\u53ef\u4ee5\u5f97\u5230\u81ea\u7136\u6570\u5012\u6570\u7684\u4efb\u610f\u5076\u6570\u6b21\u65b9\u548c\u3002\u5176\u5b9e\uff0c\u65e9\u5c31\u6709\u4eba\u505a\u8fc7\u8fd9\u6837\u7684\u5de5\u4f5c\uff0c\u4e0d\u77e5\u9053\u662f\u4e0d\u662f\u4e5f\u662f\u6b27\u62c9\u5b8c\u6210\u7684\u3002<br>$\\zeta(2k)=\\displaystyle\\sum_{n=1}^\\infty \\frac1{n^{2k}}=\\frac{(2\\pi)^{2k}(-1)^{k+1}}{2\\cdot(2k)!}B_{2k}$<br>\u2003\u2003\u8fd9\u91cc\u7684B\u53eb\u4f2f\u52aa\u5229\u6570\uff0c\u987e\u540d\u601d\u4e49\u662f\u6570\u5b66\u5bb6\u4f2f\u52aa\u5229\u53d1\u73b0\u7684\u4e00\u4e32\u6570\u5217\u3002\u8fd9\u4e2a\u6570\u5217\u5728\u5f88\u591a\u9886\u57df\u90fd\u6709\u91cd\u8981\u7684\u5e94\u7528\uff0c\u672c\u8eab\u4e5f\u6709\u5f88\u591a\u5947\u5999\u7684\u6027\u8d28\uff0c\u6709\u673a\u4f1a\u4e13\u95e8\u6765\u8bf4\u8bf4\u3002\u8fd8\u8bb0\u5f97\u62c9\u739b\u52aa\u91d1\uff081887.12.22-1920.4.26\uff09\u5728\u5370\u5ea6\u672c\u571f\u53d1\u8868\u7684\u7b2c\u4e00\u7bc7\u8bba\u6587\u7684\u540d\u5b57\u5417\uff1f\u5c31\u53eb\u300a\u8bba\u4f2f\u52aa\u5229\u6570\u7684\u4e00\u4e9b\u6027\u8d28\u300b\u3002\u8fd9\u4e2a\u62c9\u739b\u52aa\u91d1\u662f\u4e00\u4e2a\u5370\u5ea6\u5929\u624d\u6570\u5b66\u5bb6\uff0c\u4ed6\u7ed9\u51fa\u7684\u8ba1\u7b97\u03c0\u7684\u516c\u5f0f\u4ee4\u4eba\u62cd\u6848\u53eb\u7edd\uff1a<br>$\\displaystyle\\frac1\\pi=\\frac{2\\sqrt2}{9801} \\sum_{k=0}^\\infty \\frac{4k!(1103+26390k)}{{(k!)^4}396^{4k}}$<br>\u2003\u2003\u65e2\u7136\u80fd\u6c42\u51fa\u6765\u6240\u6709\u81ea\u7136\u6570\u5012\u6570\u7684\u5076\u6570\u6b21\u65b9\u548c\uff0c\u90a3\u4e48\u5947\u6570\u6b21\u65b9\u548c\u5462\uff1f\u770b\u8d77\u6765\u597d\u50cf\u4e5f\u5e76\u4e0d\u662f\u90a3\u4e48\u201c\u56f0\u96be\u201d\u3002\u524d\u9762\u5206\u6790\u8fc7\uff0c\u6b27\u62c9\u7684\u65b9\u6cd5\u662f\u65e0\u6cd5\u6c42\u51fa\u5947\u6570\u6b21\u65b9\u548c\u7684\uff0c\u5f88\u591a\u4eba\u90fd\u94bb\u7814\u8fc7\u8fd9\u4e2a\u95ee\u9898\uff0c\u7136\u800c\u65e0\u4e00\u4f8b\u5916\uff0c\u6ca1\u6709\u4eba\u5f97\u51fa\u8fc7\u89e3\u6790\u503c\u3002\u65e0\u8bba\u7528\u4ec0\u4e48\u65b9\u6cd5\u53bb\u8ba1\u7b97\uff0c\u6700\u540e\u8981\u4e48\u843d\u5165\u4e00\u4e2a\u6c42\u4e0d\u51fa\u539f\u51fd\u6570\u7684\u5b9a\u79ef\u5206\u5f62\u5f0f\uff0c\u8981\u4e0d\u5c31\u662f\u5f97\u5230\u4e00\u4e2a\u7b97\u4e0d\u51fa\u548c\u7684\u65e0\u7a77\u7ea7\u6570\u3002\u603b\u4e4b\uff0c\u8fd9\u4e2a\u503c\u6536\u655b\u5b58\u5728\uff0c\u4f46\u662f\u6c38\u8fdc\u6c42\u4e0d\u51fa\u89e3\u6790\u503c\u3002\u6709\u4eba\u4f1a\u7591\u95ee\u4e86\uff0c\u65e2\u7136\u786e\u5b9a\u8303\u56f4\u548c\u6536\u655b\u533a\u95f4\uff0c\u4e3a\u4ec0\u4e48\u4f1a\u6c42\u4e0d\u51fa\u51c6\u786e\u503c\u5462\uff1f<br>\u2003\u2003\u4e8b\u5b9e\u4e0a\uff0c\u8fd9\u79cd\u60c5\u51b5\u5f88\u5e38\u89c1\uff0c\u6211\u4eec\u80fd\u591f\u6c42\u51fa\u51c6\u786e\u503c\u7684\u65e0\u7a77\u7ea7\u6570\u5176\u5b9e\u662f\u975e\u5e38\u975e\u5e38\u6709\u9650\u7684\uff0c\u7edd\u5927\u591a\u6570\u65e0\u7a77\u7ea7\u6570\u5230\u6700\u540e\u600e\u4e48\u7b97\u90fd\u8fd8\u662f\u65e0\u7a77\u7ea7\u6570\u3002\u5f88\u591a\u770b\u4f3c\u7b80\u5355\u660e\u4e86\u7684\u95ee\u9898\uff0c\u5230\u6700\u540e\u4e5f\u4e0d\u4f1a\u662f\u6211\u4eec\u9884\u60f3\u7684\u7ed3\u679c\u3002\u6bd4\u5982\u692d\u5706\u7684\u5468\u957f\uff0c\u4f60\u5c31\u6ca1\u6cd5\u63d0\u51fa\u4e00\u4e2a\u786e\u5207\u7684\u8ba1\u7b97\u516c\u5f0f\uff0c\u6700\u597d\u7684\u7ed3\u679c\u4e5f\u5c31\u662f\u4e00\u5927\u5806\u6570\u503c\u548c\u692d\u5706\u53c2\u6570\u7ec4\u6210\u7684\u65e0\u7a77\u7ea7\u6570\u800c\u5df2\u3002\u6709\u5174\u8da3\u7684\u540c\u5b66\u53ef\u4ee5\u81ea\u5df1\u5c1d\u8bd5\u4e00\u4e0b\uff0c\u6240\u6709\u81ea\u7136\u6570\u5012\u6570\u7684\u7acb\u65b9\u548c\u6700\u7b80\u6d01\u7684\u7ed3\u679c\u662f\u4ec0\u4e48\u3002<br>\u2003\u2003\u6709\u610f\u601d\u7684\u662f\uff0c\u4efb\u610f\u4e24\u4e2a\u81ea\u7136\u6570\u4e92\u8d28\u7684\u6982\u7387\u662f$\\displaystyle\\frac{6}{\\pi^2}$\uff0c\u521a\u597d\u662f\u5df4\u585e\u5c14\u7ea7\u6570\u548c\u7684\u5012\u6570\u3002<br>\u2003\u2003\u6b27\u62c9\u5bf9\u4e8e\u5df4\u585e\u5c14\u7ea7\u6570\u7684\u7814\u7a76\uff0c\u4e5f\u7ed9\u4e86\u9ece\u66fc\u6781\u5927\u7684\u542f\u53d1\u3002\u9ece\u66fc\u5c06k\u4ece\u6574\u6570\u57df\u6269\u5c55\u5230\u590d\u6570\u57dfs\uff0c\u5e76\u7ecf\u8fc7\u89e3\u6790\u5ef6\u62d3\u548c\u4e00\u7cfb\u5217\u53d8\u6362\uff0c\u6700\u7ec8\u8bde\u751f\u4e86\u6570\u5b66\u53f2\u4e0a\u6700\u91cd\u8981\u7684\u51fd\u6570\u4e4b\u4e00\u7684\u9ece\u66fc$\\zeta$\u51fd\u6570\u3002<br>$\\zeta(s)=\\displaystyle\\sum_{n=1}^\\infty\\frac1{n^s}=\\frac1{1^s}+\\frac1{2^s}+\\frac1{3^s}+\\frac1{4^s}+\\dots+\\frac1{n^s}$<\/p><\/div>\n<\/div><\/div><\/div>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u2003\u20031644\u5e74\u745e\u58eb\u6570\u5b66\u5bb6\u76ae\u8036\u7279\u7f57\u00b7\u95e8\u6208\u5229\u63d0\u51fa\u4e86\u4e00\u4e2a\u95ee\u9898\uff0c\u6240\u6709\u81ea\u7136\u6570\u5012\u6570\u7684\u5e73\u65b9\u548c\u662f\u591a\u5c11\uff1f\u8fd9\u5c31\u662f\u6570\u5b66\u5386\u53f2\u4e0a\u8457\u540d\u7684\u201c [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3,4],"tags":[],"class_list":["post-157","post","type-post","status-publish","format-standard","hentry","category-3","category-4"],"_links":{"self":[{"href":"https:\/\/big-tan.top\/index.php?rest_route=\/wp\/v2\/posts\/157","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/big-tan.top\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/big-tan.top\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/big-tan.top\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/big-tan.top\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=157"}],"version-history":[{"count":0,"href":"https:\/\/big-tan.top\/index.php?rest_route=\/wp\/v2\/posts\/157\/revisions"}],"wp:attachment":[{"href":"https:\/\/big-tan.top\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=157"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/big-tan.top\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=157"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/big-tan.top\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=157"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}