[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/1473#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/1473","headline":"\u6570\u5024\u7d71\u5408 &#8211; \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2\u3001\u7121\u6599\u200b\u200b\u767e\u79d1\u4e8b\u5178","name":"\u6570\u5024\u7d71\u5408 &#8211; \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2\u3001\u7121\u6599\u200b\u200b\u767e\u79d1\u4e8b\u5178","description":"before-content-x4 \u6570\u5024\u7d71\u5408 &#8211; \u6570\u5024\u65b9\u6cd5 [\u521d\u3081] \u30de\u30fc\u30af\u3055\u308c\u305f\u7a4d\u5206\u306e\u8fd1\u4f3c\u8a08\u7b97\u3067\u69cb\u6210\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u7de0\u3081\u5207\u308a \u6570\u5024\u7684\u56db\u80a2 \u3001\u591a\u304f\u306e\u5834\u5408 Quadratura \u3001\u7279\u306b1\u6b21\u5143\u7a4d\u5206\u306b\u95a2\u9023\u3057\u3066\u3001\u6570\u5024\u7a4d\u5206\u3068\u540c\u7fa9\u3067\u3059\u3002 2\u6b21\u5143\u304a\u3088\u3073\u591a\u6b21\u5143\u306e\u7d71\u5408\u3068\u547c\u3070\u308c\u308b\u3053\u3068\u3082\u3042\u308a\u307e\u3059 \u7acb\u65b9\u4f53 \u3001\u540d\u524d\u3067\u3059\u304c Quadratura \u307e\u305f\u3001\u9ad8\u6b21\u5143\u3067\u306e\u7d71\u5408\u306b\u3082\u9069\u7528\u3055\u308c\u307e\u3059\u3002 after-content-x4 \u5358\u7d14\u306a\u6570\u5024\u7a4d\u5206\u65b9\u6cd5\u306f\u3001\u3044\u304f\u3064\u304b\u306e\u30dd\u30a4\u30f3\u30c8\u3067\u306e\u7a4d\u5206\u95a2\u6570\u306e\u52a0\u91cd\u5024\u306e\u9069\u5207\u306a\u5408\u8a08\u3068\u7a4d\u5206\u3092\u8fd1\u4f3c\u3059\u308b\u3053\u3068\u306b\u69cb\u6210\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u3088\u308a\u6b63\u78ba\u306a\u8fd1\u4f3c\u3092\u53d6\u5f97\u3059\u308b\u305f\u3081\u306b\u3001\u7d71\u5408\u9593\u306e\u7d71\u5408\u306f\u5c0f\u3055\u306a\u30d5\u30e9\u30b0\u30e1\u30f3\u30c8\u306b\u5206\u5272\u3055\u308c\u307e\u3059\u3002\u6700\u7d42\u7d50\u679c\u306f\u3001\u500b\u3005\u306e\u30b5\u30dd\u30fc\u30c8\u306e\u5b8c\u5168\u306a\u63a8\u5b9a\u5024\u306e\u5408\u8a08\u3067\u3059\u3002\u307b\u3068\u3093\u3069\u306e\u5834\u5408\u3001\u30b3\u30f3\u30d1\u30fc\u30c8\u30e1\u30f3\u30c8\u306f\u5e73\u7b49\u306a\u30b5\u30dd\u30fc\u30c8\u306b\u5206\u5272\u3055\u308c\u307e\u3059\u304c\u3001\u3088\u308a\u6d17\u7df4\u3055\u308c\u305f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u3001\u95a2\u6570\u306e\u5909\u52d5\u901f\u5ea6\u306b\u30b9\u30c6\u30c3\u30d7\u3092\u9069\u5408\u3055\u305b\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 Quadratur\u30e1\u30bd\u30c3\u30c9\u306e\u6700\u3082\u5358\u7d14\u306a\u65b9\u6cd5\u306f\u3001\u30d1\u30bf\u30fc\u30f3\u3092\u4f7f\u7528\u3059\u308b\u3053\u3068\u3067\u3059 after-content-x4 \u222b","datePublished":"2020-01-18","dateModified":"2020-01-18","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/e\/ea\/Integration_rectangle.png","url":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/e\/ea\/Integration_rectangle.png","height":"110","width":"340"},"url":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/1473","wordCount":19386,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4\u6570\u5024\u7d71\u5408  &#8211; \u6570\u5024\u65b9\u6cd5 [\u521d\u3081] \u30de\u30fc\u30af\u3055\u308c\u305f\u7a4d\u5206\u306e\u8fd1\u4f3c\u8a08\u7b97\u3067\u69cb\u6210\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u7de0\u3081\u5207\u308a \u6570\u5024\u7684\u56db\u80a2 \u3001\u591a\u304f\u306e\u5834\u5408 Quadratura \u3001\u7279\u306b1\u6b21\u5143\u7a4d\u5206\u306b\u95a2\u9023\u3057\u3066\u3001\u6570\u5024\u7a4d\u5206\u3068\u540c\u7fa9\u3067\u3059\u3002 2\u6b21\u5143\u304a\u3088\u3073\u591a\u6b21\u5143\u306e\u7d71\u5408\u3068\u547c\u3070\u308c\u308b\u3053\u3068\u3082\u3042\u308a\u307e\u3059 \u7acb\u65b9\u4f53 \u3001\u540d\u524d\u3067\u3059\u304c Quadratura \u307e\u305f\u3001\u9ad8\u6b21\u5143\u3067\u306e\u7d71\u5408\u306b\u3082\u9069\u7528\u3055\u308c\u307e\u3059\u3002        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u5358\u7d14\u306a\u6570\u5024\u7a4d\u5206\u65b9\u6cd5\u306f\u3001\u3044\u304f\u3064\u304b\u306e\u30dd\u30a4\u30f3\u30c8\u3067\u306e\u7a4d\u5206\u95a2\u6570\u306e\u52a0\u91cd\u5024\u306e\u9069\u5207\u306a\u5408\u8a08\u3068\u7a4d\u5206\u3092\u8fd1\u4f3c\u3059\u308b\u3053\u3068\u306b\u69cb\u6210\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u3088\u308a\u6b63\u78ba\u306a\u8fd1\u4f3c\u3092\u53d6\u5f97\u3059\u308b\u305f\u3081\u306b\u3001\u7d71\u5408\u9593\u306e\u7d71\u5408\u306f\u5c0f\u3055\u306a\u30d5\u30e9\u30b0\u30e1\u30f3\u30c8\u306b\u5206\u5272\u3055\u308c\u307e\u3059\u3002\u6700\u7d42\u7d50\u679c\u306f\u3001\u500b\u3005\u306e\u30b5\u30dd\u30fc\u30c8\u306e\u5b8c\u5168\u306a\u63a8\u5b9a\u5024\u306e\u5408\u8a08\u3067\u3059\u3002\u307b\u3068\u3093\u3069\u306e\u5834\u5408\u3001\u30b3\u30f3\u30d1\u30fc\u30c8\u30e1\u30f3\u30c8\u306f\u5e73\u7b49\u306a\u30b5\u30dd\u30fc\u30c8\u306b\u5206\u5272\u3055\u308c\u307e\u3059\u304c\u3001\u3088\u308a\u6d17\u7df4\u3055\u308c\u305f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u3001\u95a2\u6570\u306e\u5909\u52d5\u901f\u5ea6\u306b\u30b9\u30c6\u30c3\u30d7\u3092\u9069\u5408\u3055\u305b\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 Quadratur\u30e1\u30bd\u30c3\u30c9\u306e\u6700\u3082\u5358\u7d14\u306a\u65b9\u6cd5\u306f\u3001\u30d1\u30bf\u30fc\u30f3\u3092\u4f7f\u7528\u3059\u308b\u3053\u3068\u3067\u3059        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u222b x0xnf \uff08 \u30d0\u30c4 \uff09\uff09 \u2248 h \u2211 i=0n\u22121f \uff08 \u30d0\u30c4 i+ a h \uff09\uff09 \u3001 h = xn\u2212x0n\u3001 {displaystyle int _ {x_ {0}}^{x_ {n}} !! !! f\uff08x\uff09hsum _ {i = 0}^{n-1} f\uff08x_ {i}+alpha h\uff09\u3001quad h = {tfrac {x_ {n} -x_ {} {0}}}}}}} \u305d\u3053\u306b n {displaystyle n} \u9577\u3055\u306e\u591a\u304f\u306e\u30b5\u30dd\u30fc\u30c8\u3067\u3059 h \u3002 {displaystyle h\u3002}  \u3053\u306e\u65b9\u6cd5\u306b\u306f3\u3064\u306e\u30d0\u30ea\u30a8\u30fc\u30b7\u30e7\u30f3\u304c\u3042\u308a\u307e\u3059\u3002        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u5de6\u306e\u9577\u65b9\u5f62 a = 0 \u3001 {displaystyle alpha = 0\u3001} \u4e2d\u7a0b\u5ea6\u306e\u9577\u65b9\u5f62 a = 12{displaystyle alpha = {tfrac {1} {2}}}  &#8211; \u3053\u306e\u30d0\u30ea\u30a2\u30f3\u30c8\u306f\u6700\u9069\u306a\u8fd1\u4f3c\u3092\u4e0e\u3048\u307e\u3059\u3001 \u6b63\u3057\u3044\u9577\u65b9\u5f62\u304c\u3044\u3064 a = \u521d\u3081\u3002 {displaystyle alpha = 1\u3002} \u3082\u3061\u308d\u3093\u3001\u4e00\u822c\u7684\u306a\u30d0\u30ea\u30a2\u30f3\u30c8\u304c\u3042\u308a\u307e\u3059 a \u2208 [ 0 \u3001 \u521d\u3081 ] \u3002 {[0\u30011]\u306edisplaystyle alpha\u3002}  \u53f0\u5f62\u6cd5\u306f\u3001\u5404\u30b5\u30dd\u30fc\u30c8\u306e\u7a4d\u5206\u95a2\u6570\u306b\u8fd1\u4f3c\u3057\u3066\u3044\u308b\u3053\u3068\u3067\u3059 \u30d0\u30c4 \u79c1 + \u521d\u3081 \u3001 \u30d0\u30c4 \u79c1 \u3001 \u79c1 = 0 \u3001 \u521d\u3081 \u3001 &#8230; n  &#8211;  \u521d\u3081 {displaystyle x_ {i+1} ,, x_ {i}\u3001; i = 0 \u3001\u3001 1\u3001\u3001dots\u3001n-1} \u9577\u3055\u3067 h = xn\u2212x0n\u3002 {displaystyle h = {tfrac {x_ {n} -x_ {0}} {n}}}}}} \u3053\u308c\u306b\u3088\u308a\u3001\u30de\u30fc\u30ad\u30f3\u30b0\u3092\u5165\u529b\u3057\u305f\u5f8c\u306b\u53d7\u3051\u53d6\u308a\u307e\u3059 f \u79c1 \u559c\u3093\u3067 f \uff08 \u30d0\u30c4 \u79c1 \uff09\uff09 {displaystyle f_ {i} equiv f\uff08x_ {i}\uff09}  \u222b x0xnf \uff08 \u30d0\u30c4 \uff09\uff09 d \u30d0\u30c4 \u2248 \u2211 i=0n\u22121h2[ f \uff08 \u30d0\u30c4 i+1\uff09\uff09 + f \uff08 \u30d0\u30c4 i\uff09\uff09 \uff09\uff09 ] = h \uff08 12f 0+ f 1+ f 2+ &#8230; + f n\u22121+ 12f n\uff09\uff09 \u3002 {displaystyle int _ {x_ {0}}^{x_ {n}} !! f\uff08x\uff09dxapprox sum _ {i = 0}^{n-1} {tfrac {h} {2}}}}} [f\uff08x_ {i+1}\uff09+f\uff08x_ {{i}\uff09}}}}}}}\uff09 _ {0}+f_ {1}+f_ {2}+\u3001\u30c9\u30c3\u30c8\u3001+f_ {n-1}+{tfrac {1} {2}} f_ {n}\uff09\u3002}} \u3053\u306e\u65b9\u6cd5\u306e\u30a8\u30e9\u30fc\u306e\u63a8\u5b9a\u306f\u3067\u3059 r n= | \u222babf(x)dx\u2212Sn| \u2a7d (b\u2212a)3M\u2032\u203212n2\u3001 {displaystyle r_ {n} = left | int limits _ {a}^{b} f\uff08x\uff09dx-s_ {n}\u53f3| leqslant {frac {\uff08b-a\uff09^{3} m &#8216;{&#8216;}} {12n^{2}}}}}}} \u3069\u3053\uff1a m &#8216; \u2032= \u30de\u30c3\u30af\u30b9 \u27e8a,b\u27e9| f &#8216; \u2032| \u3002 {displaystyle m &#8216;{&#8216;} = max _ {langle a\u3001brangle} | f &#8216;{&#8216;} |\u3002}  \u5225\u306e\u8a18\u4e8b\uff1aSimpson\u30e1\u30bd\u30c3\u30c9\u3002 \u3053\u306e\u65b9\u6cd5\u3067\u306f\u3001\u5076\u6570\u306b\u7d71\u5408\u306e\u5206\u5272\u304c\u5fc5\u8981\u3067\u3059 2 n {displaystyle 2n} \u30b5\u30dd\u30fc\u30c8\u3001\u3064\u307e\u308a h = x2n\u2212x02n\u3001 {displaystyle h = {frac {x_ {2n} -x_ {0}} {2n}}\u3001} f i= f \uff08 \u30d0\u30c4 i\uff09\uff09 \u3001 \u30d0\u30c4 i= \u30d0\u30c4 0+ \u79c1 h \u3001 \u79c1 = 0 \u3001 \u521d\u3081 \u3001 &#8230; 2 n \u3002 {displaystyle f_ {i} = f\uff08x_ {i}\uff09\u3001quad x_ {i} = x_ {0}+ih\u3001quad i = 0\u30011\u3001\u3001dots\u30012n\u3002} 2\u3064\u306e\u96a3\u63a5\u3059\u308b\u30b5\u30dd\u30fc\u30c8\u306b\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u306e\u6b63\u65b9\u5f62\u306e\u88dc\u9593\u3092\u4f7f\u7528\u3059\u308b\u3068\u3001 \u222b xixi+2f \uff08 \u30d0\u30c4 \uff09\uff09 d \u30d0\u30c4 \u2248 h3[ f i+ 4 f i+1+ f i+2] \u3001 {displaystyle int _ {x_ {i}}^{x_ {i+2}} f\uff08x\uff09dxapprox {tfrac {h} {3}} [f_ {i}+4f_ {i+1}+f_ {i+2}]\u3001} \u222b x0x2nf \uff08 \u30d0\u30c4 \uff09\uff09 d \u30d0\u30c4 \u2248 h3[ f 0+ f 2n+ 4 \uff08 f 1+ f 3+ &#8230; + f 2n\u22121\uff09\uff09 + 2 \uff08 f 2+ f 4+ &#8230; f 2n\u22122\uff09\uff09 ] \u3002 {displaystyle int _ {x_ {0}}^{x_ {2n}} f\uff08x\uff09dxapprox {tfrac {h} {3}} [f_ {0}+f_ {2n} +4\uff08f_ {1}+f_ {2n-1} {2n-1}+ {4}+\u3001\u30c9\u30c3\u30c8\u3001f_ {2n-2}\uff09]\u3002} \u6a5f\u80fd\u3067\u3044\u3063\u3071\u3044\u306e\u5834\u5408 f \uff08 \u30d0\u30c4 \uff09\uff09 \u2208 c \uff08 4 \uff09\uff09 {displaystyle f\uff08x\uff09in c^{\uff084\uff09}} \u30b3\u30f3\u30d1\u30fc\u30c8\u30e1\u30f3\u30c8\u5185 [ a \u3001 b ] {displaystyle [a ,, b]} \u30e1\u30bd\u30c3\u30c9\u306e\u65b9\u6cd5\u306f\u3067\u3059 r =  &#8211;  (b\u2212a)h4180f IV\uff08 \u30d0\u30c4 \uff09\uff09 \u3001 \u30d0\u30c4 \u2208 [ a \u3001 b ] \u3002 {displaystyle r =  &#8211;  {tfrac {\uff08b-a\uff09h^{4}} {180}} f^{iv}\uff08x\uff09\u3001quad xin [a ,, b]\u3002}}  \u5225\u306e\u8a18\u4e8b\uff1a\u30ac\u30a6\u30b9\u8c61\u9650\u3002 Gauss\u30e1\u30bd\u30c3\u30c9\u3092\u4f7f\u7528\u3059\u308b\u3068\u3001\u56db\u89d2\u8a2d\u8a08\u306e\u7cbe\u5ea6\u306e\u5927\u5e45\u306a\u5897\u52a0\u3092\u53d6\u5f97\u3067\u304d\u307e\u3059 [\u521d\u3081] \u3002\u305d\u306e\u672c\u8cea\u306f\u3001\u30ce\u30fc\u30c9\u306e\u4f4d\u7f6e\u3092\u6700\u9069\u306b\u9078\u629e\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u6b63\u65b9\u5f62\u30a8\u30e9\u30fc\u3092\u6700\u5c0f\u5316\u3059\u308b\u3053\u3068\u306b\u3042\u308a\u307e\u3059 \u30d0\u30c4 \u79c1 {displaystyle xi _ {i}} \u304a\u3088\u3073\u91cd\u91cf\u5024 w\u00af\u79c1 {displaystyle {overline {w}} _ {i}} \u8c61\u9650\u30d1\u30bf\u30fc\u30f3 I(f)=\u222babf(x)dx=b\u2212a2\u222b\u221211F(\u03be)d\u03be=b\u2212a2\u2211i=1nw\u00afiF(\u03bei),{displaystyle I(f)=int _{a}^{b}!!f(x)dx={tfrac {b-a}{2}}int _{-1}^{1}F(xi )dxi ={tfrac {b-a}{2}}sum _{i=1}^{n}{overline {w}}_{i}F(xi _{i}),} \uff08a\uff09 \u305d\u3053\u306b f \uff08 \u30d0\u30c4 \uff09\uff09 = f \uff08 a+b2+ b\u2212a2\u30d0\u30c4 \uff09\uff09 \u3001 d \u30d0\u30c4 = b\u2212a2d \u30d0\u30c4 \u3002 {displaystyle f\uff08xi\uff09= f\uff08{tfrac {a+b} {2} {2}}+{tfrac {b-a} {2}} xi\uff09\u3001quad dx = {tfrac {b-a} {2}} dxi\u3002}}}  \u30d5\u30a9\u30fc\u30df\u30e5\u30e9\u3067\u4f7f\u7528\u3055\u308c\u3066\u3044\u308b\u30c7\u30b6\u30a4\u30f3\u306e\u304a\u304b\u3052\u3067\uff08a\uff09 \u30d0\u30c4 = a+b2+ b\u2212a2\u30d0\u30c4 {displaystyle x = {tfrac {a+b} {2}}+{tfrac {b-a} {2}} xi} \u4efb\u610f\u306e\u30b3\u30f3\u30d1\u30fc\u30c8\u30e1\u30f3\u30c8 \uff08 a \u3001 b \uff09\uff09 {displaystyle\uff08a ,, b\uff09} \u6a19\u6e96\u30b3\u30f3\u30d1\u30fc\u30c8\u30e1\u30f3\u30c8\u7528 \uff08  &#8211;  \u521d\u3081 \u3001 \u521d\u3081 \uff09\uff09 \u3001 {displaystyle\uff08-1\u30011\uff09\u3001} \u3053\u306e\u30d1\u30bf\u30fc\u30f3\u306f\u3001\u4e00\u610f\u306e\u5024\u306e\u305f\u3081\u666e\u904d\u7684\u3067\u3059 w\u00af\u79c1 \u3001 \u30d0\u30c4 \u79c1 {displaystyle {overline {w}} _ {i} ,, xi _ {i}} \u3042\u306a\u305f\u306f\u5b8c\u5168\u306b\u5b89\u5b9a\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 \u5024\u306e\u8a08\u7b97 w\u00af\u79c1 \u3001 \u30d0\u30c4 \u79c1 \u3001 \u79c1 = \u521d\u3081 \u3001 2 \u3001 &#8230; \u3001 n {displaystyle {overline {w}} _ {i} ,, xi _ {i}\u3001; i = 1 \u3001\u3001 2 \u3001\u3001 dots ,, n} \u30b7\u30f3\u30b0\u30eb\u306e\u30ac\u30a6\u30b9\u624b\u9806\u306e\u7d71\u5408\u3092\u8981\u6c42\u3059\u308b\u3053\u3068\u3067\u5b9f\u884c\u3067\u304d\u307e\u3059 \u30d0\u30c4 k \u3001 k = 0 \u3001 \u521d\u3081 \u3001 &#8230; \u3001 2 n  &#8211;  \u521d\u3081 {displaystyle x^{k}\u3001; k = 0\u30011 \u3001\u3001 dots\u30012n-1} \u6b63\u78ba\u306a\u7d50\u679c\u3092\u51fa\u3057\u307e\u3057\u305f \u2211i=1nw\u00afi\u03beik\u2261\u222b\u221211\u03bekd\u03be{displaystyle sum _{i=1}^{n}{overline {w}}_{i}xi _{i}^{k}equiv int _{-1}^{1}!!xi ^{k}dxi } \uff08b\uff09 \u3064\u307e\u308a\u3001\u305d\u306e\u305f\u3081\u306e\u3082\u306e\u3067\u3059 k = 0 \u3001 \u521d\u3081 \u3001 &#8230; \u3001 2 n  &#8211;  \u521d\u3081 {displaystyle k = 0 \u3001\u3001 1 \u3001\u3001 dots\u30012n-1}  w\u00af1\u30d0\u30c4 1k+ w\u00af2\u30d0\u30c4 2k+ \u22ef + w\u00afn\u30d0\u30c4 nk= p k\u3001 p k= 1\u2212(\u22121)k+1k+1\u3002 {Displaystyle {overline {w}} _ {1} xi _ {1}^{k}+{overline {w}} _ {2} xi _ {2}^{k}+{Overline {w}} _ {N} xi} } = {tfrac {1-(-1)^{k+1}} {k+1}}.}. \u66f8\u3044\u305f\u5f8c\u3001\u79c1\u305f\u3061\u306f\u89e3\u6c7a\u3059\u308b\u306e\u304c\u96e3\u3057\u3044\u3001\u975e\u7dda\u5f62\u30b7\u30b9\u30c6\u30e0\u3092\u53d6\u5f97\u3057\u307e\u3059 2 n {displaystyle 2n} \u65b9\u7a0b\u5f0f w\u00af1+w\u00af2+\u22ef+w\u00afn=2,{displaystyle {overline {w}}_{1}+{overline {w}}_{2}+dots +{overline {w}}_{n}=2,}w\u00af1\u03be1+w\u00af2\u03be2+\u22ef+w\u00afn\u03ben=0,{displaystyle {overline {w}}_{1}xi _{1}+{overline {w}}_{2}xi _{2}+dots +{overline {w}}_{n}xi _{n}=0,}w\u00af1\u03be12+w\u00af2\u03be22+\u22ef+w\u00afn\u03ben2=23,{displaystyle {overline {w}}_{1}xi _{1}^{2}+{overline {w}}_{2}xi _{2}^{2}+dots +{overline {w}}_{n}xi _{n}^{2}={tfrac {2}{3}},}w\u00af1\u03be13+w\u00af2\u03be23+\u22ef+w\u00afn\u03ben3=0,{displaystyle {overline {w}}_{1}xi _{1}^{3}+{overline {w}}_{2}xi _{2}^{3}+dots +{overline {w}}_{n}xi _{n}^{3}=0,}.............................{displaystyle &#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;..}w\u00af1\u03be1k+w\u00af2\u03be2k+\u22ef+w\u00afn\u03benk={2k+1gdykjest parzyste0gdykjest nieparzyste{displaystyle {overline {w}}_{1}xi _{1}^{k}+{overline {w}}_{2}xi _{2}^{k}+dots +{overline {w}}_{n}xi _{n}^{k}={begin{cases}{tfrac {2}{k+1}};;{text{gdy}};;k;;{text{jest parzyste}}\\;;0quad {text{gdy}};;k;;{text{jest nieparzyste}}end{cases}}}.............................{displaystyle &#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;..}w\u00af1\u03be12n\u22122+w\u00af2\u03be22n\u22122+\u22ef+w\u00afn\u03ben2n\u22122=22n\u22121,{displaystyle {overline {w}}_{1}xi _{1}^{2n-2}+{overline {w}}_{2}xi _{2}^{2n-2}+dots +{overline {w}}_{n}xi _{n}^{2n-2}={tfrac {2}{2n-1}},}w\u00af1\u03be12n\u22121+w\u00af2\u03be22n\u22121+\u22ef+w\u00afn\u03ben2n\u22121=0,{displaystyle {overline {w}}_{1}xi _{1}^{2n-1}+{overline {w}}_{2}xi _{2}^{2n-1}+dots +{overline {w}}_{n}xi _{n}^{2n-1}=0,}\uff08c\uff09 \u6c7a\u5b9a 2 n {displaystyle 2n} \u5024 w\u00af\u79c1 \u3001 \u30d0\u30c4 \u79c1 \u3002 {displaystyle {overline {w}} _ {i} ,, xi _ {i}\u3002}  \u4e0b\u306e\u8868\u306b\u306f\u30b3\u30f3\u30d1\u30a4\u30eb\u3055\u308c\u3066\u3044\u307e\u3059 [2] \u8a08\u7b97\u3055\u308c\u305f\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u5024 w\u00af\u79c1 \u3001 \u30d0\u30c4 \u79c1 {displaystyle {overline {w}} _ {i} ,, xi _ {i}} \u30b9\u30c6\u30c3\u30d7\u306e\u591a\u9805\u5f0f\u306e\u5834\u5408 n \u2a7d 8\u3002 {displaystyle nleqslant 8.}  n{displaystyle {}; n; {}} \u03be1;\u03ben{displaystyle xi _ {1};\u3001xi _ {n}} \u03be2;\u03ben\u22121{displaystyle xi _ {2};\u3001xi _ {n-1}}}} \u03be3;\u03ben\u22122{displaystyle xi _ {3};\u3001xi _ {n-2}}}} \u03be4;\u03ben\u22123{displaystyle xi _ {4};\u3001xi _ {n-3}}}}  \u521d\u3081 0  2 \u22130,57735027{displaystyle mp 0 {\u3001} 57735027}  3 \u22130,77459667{displaystyle mp 0 {\u3001} 77459667} 0  4 \u22130,86113631{displaystyle mp 0 {\u3001} 86113631} \u22130,33998104{displaystyle mp 0 {\u3001} 33998104}  5 \u22130,90617985{displaystyle mp 0 {\u3001} 90617985} \u22130,53846931{displaystyle mp 0 {\u3001} 53846931} 0  6 \u22130,93246951{displaystyle mp 0 {\u3001} 93246951} \u22130,66120939{displaystyle mp 0 {\u3001} 66120939} \u22130,23861919{displaystyle mp 0 {\u3001} 23861919}  7 \u22130,94910791{displaystyle mp 0 {\u3001} 94910791} \u22130,74153119{displaystyle mp 0 {\u3001} 74153119} \u22130,40584515{displaystyle mp 0 {\u3001} 40584515} 0 8 \u22130,96028986{displaystyle mp 0 {\u3001} 96028986} \u22130,79666648{displaystyle mp 0 {\u3001} 79666648} \u22130,52553242{displaystyle mp 0 {\u3001} 52553242} \u22130,18343464{displaystyle mp 0 {\u3001} 18343464}  n{displaystyle {}; n; {}} w\u00af1;w\u00afn{displaystyle {overline {w}} _ {1};\u3001{overline {w}} _ {n}}} w\u00af2;w\u00afn\u22121{displaystyle {overline {w}} _ {2};\u3001{overline {w}} _ {n-1}} w\u00af3;w\u00afn\u22122{displaystyle {overline {w}} _ {3};\u3001{overline {w}} _ {n-2}} w\u00af4;w\u00afn\u22123{displaystyle {overline {w}} _ {4};\u3001{overline {w}} _ {n-3}}  \u521d\u3081 2{displaystyle 2}  2 1{displaystyle1}  3 0,55555556{displaystyle 0 {\u3001} 555556} 0,88888889{displaystyle 0 {\u3001} 8888889}  4 0,34785484{displaystyle 0 {\u3001} 34785484} 0,65214516{displaystyle 0 {\u3001} 65214516}  5 0,23692688{displaystyle 0 {\u3001} 23692688} 0,47862868{displaystyle 0 {\u3001} 47862868} 0,56888889{displaystyle 0 {\u3001} 56888889}  6 0,17132450{displaystyle 0 {\u3001} 17132450} 0,36076158{displaystyle 0 {\u3001} 36076158} 0,46791394{displaystyle 0 {\u3001} 46791394}  7 0,12948496{displaystyle 0 {\u3001} 12948496} 0,27970540{displaystyle 0 {\u3001} 27970540} 0,38183006{displaystyle 0 {\u3001} 38183006} 0,41795918{displaystyle 0 {\u3001} 41795918}  8 0,10122854{displaystyle 0 {\u3001} 10122854} 0,22238104{displaystyle 0 {\u3001} 22238104} 0,31370664{displaystyle 0 {\u3001} 31370664} 0,36268378{displaystyle 0 {\u3001} 36268378}  \u6587\u5b66\u3067\u5f15\u7528 [\u521d\u3081] \u65b9\u7a0b\u5f0f\u306e\u30b7\u30b9\u30c6\u30e0\u3092\u89e3\u304f\u65b9\u6cd5\uff08c\uff09\u306f\u3001\u4efb\u610f\u306e\u756a\u53f7\u306e\u6570\u5024\u306e\u5024\u306b\u3064\u3044\u3066\u305d\u308c\u3092\u89b3\u5bdf\u3059\u308b\u3053\u3068\u3067\u69cb\u6210\u3055\u308c\u3066\u3044\u307e\u3059 \u30d0\u30c4 \u521d\u3081 < \u30d0\u30c4 2 < &#8230; < \u30d0\u30c4 n {displaystyle xi _ {1} n \u3002 {displaystyle w_ {i}\u3001; i = 1\u3001\u30012\u3001\u3001dots\u3001n\u3002} \u305f\u3060\u3057\u3001\u6700\u9069\u306a\u5024\u306e\u6c7a\u5b9a\u306f\u672a\u89e3\u6c7a\u306e\u554f\u984c\u306e\u307e\u307e\u3067\u3059 \u30d0\u30c4 \u79c1 \u3002 {displaystyle xi _ {i}\u3002}  \u3053\u306e\u76ee\u7684\u306e\u305f\u3081\u306b\u3001\u6761\u4ef6\uff08b\uff09\u306f\u591a\u9805\u5f0f\u306e\u7a0b\u5ea6\u7d50\u5408\u306e\u5f62\u5f0f\u306b\u5909\u66f4\u3057\u307e\u3059 n = n + k \u3001 k = 0 \u3001 \u521d\u3081 \u3001 &#8230; \u3001 n  &#8211;  \u521d\u3081\u3002 {displaystyle n = n+k\u3001k = 0\u30011\u3001dots\u3001n-1\u3002}  \u2211i=1nwi\u03beikPn(\u03bei)\u2261\u222b\u221211\u03bekPn(\u03be)d\u03be,k=0,1,\u2026n\u22121,{displaystyle sum _{i=1}^{n}w_{i}xi _{i}^{k}P_{n}(xi _{i})equiv int _{-1}^{1}!!xi ^{k}P_{n}(xi )dxi ,quad k=0,,1,,dots ,n-1,}\uff08d\uff09 \u3069\u3053 p n \uff08 \u30d0\u30c4 \uff09\uff09 {displaystyle p_ {n}\uff08x\uff09} \u7a0b\u5ea6\u591a\u9805\u5f0f\u3067\u3059 n \u3002 {displaystyle n\u3002}  \u5f0f\uff08d\uff09\u306e\u7a4d\u5206\u306f\u3001\u30de\u30eb\u30c1\u30b3\u30a2\u306e\u3068\u304d\u306b\u58ca\u308c\u307e\u3059 p n \uff08 \u30d0\u30c4 \uff09\uff09 {displaystyle p_ {n}\uff08x\uff09} \u5f7c\u3089\u306f\u30b7\u30f3\u30b0\u30eb\u30df\u30a2\u30f3\u3068\u306e\u76f4\u4ea4\u3067\u3059 \u30d0\u30c4 k {displaystyle x^{k}} \u305f\u3081\u306b k < n \u3001 {displaystyle k \u306b \u30d0\u30c4 \u2208 \uff08  &#8211;  \u521d\u3081 \u3001 \u521d\u3081 \uff09\uff09 \u3002 {displaystylexin\uff08-1\u3001\u30011\uff09\u3002} \u307e\u3055\u306b\u305d\u306e\u30d7\u30ed\u30d1\u30c6\u30a3 [3] \u5f7c\u3089\u306flegendre Multi -Multi\u3092\u6301\u3063\u3066\u3044\u307e\u3059\u3002\u5f7c\u3089\u306e\u305f\u3081\u306b\uff08d\uff09\u306e\u4ee3\u308f\u308a\u306b\u6301\u3063\u3066\u3044\u307e\u3059 \u2211i=1nwi\u03beikPn(\u03bei)\u22610,k=0,1,\u2026n\u22121.{displaystyle sum _{i=1}^{n}w_{i}xi _{i}^{k}P_{n}(xi _{i})equiv 0,quad k=0,,1,,dots ,n-1.}\uff08\u305d\u3046\u3067\u3059\uff09 \u3053\u306e\u6761\u4ef6\u306f\u3001\u4efb\u610f\u306e\u5024\u306b\u5bfe\u3057\u3066\u8b58\u5225\u3055\u308c\u307e\u3059 \u306e \u79c1 \u3001 {displaystyle w_ {i}\u3001} \u3044\u3064 \u30d0\u30c4 \u79c1 {displaystyle xi _ {i}} \u305d\u308c\u3089\u306fLegendRe Polynomial\u306e\u8981\u7d20\u3067\u3059 n {displaystyle n}  &#8211; \u3053\u306e\u7a0b\u5ea6\u3001\u6b21\u306b p n \uff08 \u30d0\u30c4 \u79c1 \uff09\uff09 \u559c\u3093\u3067 0 \u3001 \u79c1 = \u521d\u3081 \u3001 2 \u3001 &#8230; n \u3002 {displaystyle p_ {n}\uff08xi _ {i}\uff09equiv 0\u3001; i = 1\u30012\u3001\u3001dots\u3001n\u3002}  \u78ba\u7387\u7684\u65b9\u6cd5\u306f\u3001\u30de\u30fc\u30af\u3055\u308c\u305f\u7a4d\u5206\u306e\u8fd1\u4f3c\u8a08\u7b97\u306b\u3082\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002\u305f\u3060\u3057\u3001\u3053\u306e\u3088\u3046\u306a\u7d71\u5408\u306e\u7d50\u679c\u3082\u30e9\u30f3\u30c0\u30e0\u5909\u6570\u3067\u3042\u308b\u3053\u3068\u3092\u899a\u3048\u3066\u304a\u304f\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002 \u3053\u306e\u30a2\u30a4\u30c7\u30a2\u306f\u3001\u6a5f\u80fd\u30c1\u30e3\u30fc\u30c8\u306e\u4e0b\u306b\u3042\u308b\u30d5\u30a3\u30fc\u30eb\u30c9\u306e\u30d5\u30a3\u30fc\u30eb\u30c9\u306b\u57fa\u3065\u3044\u3066\u3044\u307e\u3059 0}&#8221;>\u30c1\u30e3\u30fc\u30c8\u306e\u4e0a\u306e\u30d5\u30a3\u30fc\u30eb\u30c9\u3092\u5dee\u3057\u5f15\u304d\u307e\u3059 f \uff08 \u30d0\u30c4 \uff09\uff09 < 0 {displaystyle f\uff08x\uff09b\u2212an\u2211i=1nf(xi),{displaystyle int limits _ {a}^{b} f\uff08x\uff09dxapprox {frac {b-a} {n}} sum _ {i = 1}^{n} f\uff08x_ {i}\uff09\u3001} \u30d0\u30c4 i{displaystyle x_ {i}} \u30b3\u30f3\u30d1\u30fc\u30c8\u30e1\u30f3\u30c8\u304b\u3089\u30e9\u30f3\u30c0\u30e0\u306b\u9078\u629e\u3055\u308c\u307e\u3059 n {displaystyle n} \u30b5\u30f3\u30d7\u30eb\u756a\u53f7\u3092\u6307\u5b9a\u3057\u307e\u3059\u3002 \u4f8b &#8211; \u9577\u65b9\u5f62\u306e\u65b9\u6cd5 [ \u7de8\u96c6 | \u30b3\u30fc\u30c9\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u95a2\u6570\u3092\u30de\u30fc\u30b8\u3057\u3066\u307f\u307e\u3057\u3087\u3046 cos \u2061 \uff08 \u30d0\u30c4 \uff09\uff09 {displaystyle cos\uff08x\uff09} 0\u304b\u30891\u306e\u7bc4\u56f2\u3067\u306f\u3001\u5206\u6790\u7684\u306b\u30de\u30fc\u30b8\u3067\u304d\u308b\u305f\u3081\u3001\u6b63\u78ba\u306a\u7d50\u679c\u304c\u308f\u304b\u3063\u3066\u3044\u308b\u305f\u3081\u3001\u3055\u307e\u3056\u307e\u306a\u7d71\u5408\u65b9\u6cd5\u3092\u8fd1\u4f3c\u3059\u308b\u30a8\u30e9\u30fc\u3092\u7c21\u5358\u306b\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002 10\u5c0f\u6570\u70b9\u306e\u6b63\u78ba\u3055\u3067\u3001\u6b63\u3057\u3044\u7d50\u679c\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002 \u222b 01cos \u2061 \uff08 \u30d0\u30c4 \uff09\uff09 d \u30d0\u30c4 = \u7f6a \u2061 \uff08 \u521d\u3081 \uff09\uff09  &#8211;  \u7f6a \u2061 \uff08 0 \uff09\uff09 = 0.841 4709848\u3002 {displaystyle int limits _ {0}^{1} cos\uff08x\uff09dx = sin\uff081\uff09-sin\uff080\uff09= 0 {\u3001} 8414709848\u3002}} \u30df\u30c9\u30eb\u30dd\u30a4\u30f3\u30c8\u306e\u539f\u7406\u3092\u4f7f\u7528\u3057\u305f\u6570\u5024\u7d71\u5408\u306b\u3088\u308a\u3001\u7d50\u679c\u304c\u5f97\u3089\u308c\u307e\u3059\u3002 \u222b 01cos \u2061 \uff08 \u30d0\u30c4 \uff09\uff09 d \u30d0\u30c4 \u2248 \uff08 \u521d\u3081  &#8211;  0 \uff09\uff09 cos \u2061 \uff08 12\uff09\uff09 = 0.877 5825619 \u3001 {displaystyle int limits _ {0}^{1} cos\uff08x\uff09dxapprox\uff081-0\uff09cos left\uff08{frac {1} {2}}\u53f3\uff09= 0 {\u3001} 8775825619\u3001} \u3053\u308c\u306b\u3088\u308a\u30010.0361115771\uff08\u76f8\u5bfe\u8aa4\u5dee4.3\uff05\uff09\u304c\u3042\u308a\u307e\u3059 &#8211; \u3053\u306e\u3088\u3046\u306a\u5358\u7d14\u306a\u65b9\u6cd5\u3067\u306f\u5c0f\u3055\u3044\u3067\u3059\u304c\u3001\u3082\u3061\u308d\u3093\u591a\u304f\u306e\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u306b\u306f\u4e0d\u5341\u5206\u3067\u3059\u3002 \u3088\u308a\u826f\u3044\u8fd1\u4f3c\u3092\u53d6\u5f97\u3059\u308b\u305f\u3081\u306b\u3001\u7d71\u5408\u30b3\u30f3\u30d1\u30fc\u30c8\u30e1\u30f3\u30c8\u3092\u5206\u5272\u3067\u304d\u307e\u3059\u3002 \u222b 01cos \u2061 \uff08 \u30d0\u30c4 \uff09\uff09 d \u30d0\u30c4 = \u222b 01\/2cos \u2061 \uff08 \u30d0\u30c4 \uff09\uff09 d \u30d0\u30c4 + \u222b 1\/21cos \u2061 \uff08 \u30d0\u30c4 \uff09\uff09 d \u30d0\u30c4 \u2248 {displaystyle int limits _ {0}^{1} cos\uff08x\uff09dx = int limits _ {0}^{1\/2} cos\uff08x\uff09dx+int limits _ {1\/2}^{1} cos\uff08x\uff09dxapprox} \u2248 \uff08 12 &#8211;  0 \uff09\uff09 cos \u2061 \uff08 14\uff09\uff09 + \uff08 \u521d\u3081  &#8211;  12\uff09\uff09 cos \u2061 \uff08 34\uff09\uff09 = 0.850 3006452 {displaystyle {} quad reft\uff08{frac {1} {2}} -0right\uff09cos left\uff08{frac {1} {4}}\u53f3\uff09+\u5de6\uff081- {frac {1} {2}}\u53f3\uff09  \u7d76\u5bfe\u8aa4\u5dee0.0088296604\u307e\u305f\u306f\u76f8\u5bfe1\uff05\u3002 \u3088\u308a\u591a\u304f\u306e\u30d5\u30e9\u30b0\u30e1\u30f3\u30c8\u9593\u3067\u7d71\u5408\u3092\u5206\u5272\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u3088\u308a\u826f\u3044\u8fd1\u4f3c\u5024\u3092\u53d6\u5f97\u3067\u304d\u307e\u3059\u3002 \u756a\u53f7 \u90e8 \u7d50\u679c \u9593\u9055\u3044 \u7d76\u5bfe \u76f8\u5bfe\u7684 \u521d\u3081 0.8775825619 0.0361115771 4.29\uff05 2 0.8503006452 0.0088296604 1.05\uff05 4 0.8436663168 0.0021953320 0.26\uff05 8 0.8420190672 0.0005480824 0.07\uff05 0.8414709848 0 0\uff05 \u4f8b2 [ \u7de8\u96c6 | \u30b3\u30fc\u30c9\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u6642\u9593\u7d4c\u904e\u306e\u6570\u5024\u7d71\u5408\u3002\u30c8\u30e9\u30a4\u30a2\u30eb\u3092\u7d71\u5408\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002 \u7f6a \u2061 \uff08 t \uff09\uff09 {displaystyle sin\uff08t\uff09} 0\u304b\u30890\u304b\u3089 4 de pi {displaystyle 4cdot pi} [s]\u3002\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u306e\u983b\u5ea6\u3092\u30de\u30fc\u30af\u3057\u307e\u3057\u3087\u3046 f p {displaystyle f_ {p}} [Hz]\u3002 \u8a08\u7b97\u306b\u306f\u9577\u65b9\u5f62\u306e\u65b9\u6cd5\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002\u5206\u5272\u76f4\u5f84 t p = \u521d\u3081 fp= t \u79c1 + \u521d\u3081  &#8211;  t \u79c1 {displaystyle t_ {p} = {frac {1} {f_ {p}}} = t_ {i+1} -t_ {i}} 1. \u30d0\u30c4 \u79c1 \uff08 t \uff09\uff09 {displaystyle x_ {i}\uff08t\uff09} \u7d71\u5408\u5f8c\u306e\u30b5\u30f3\u30d7\u30eb\u3092\u610f\u5473\u3057\u307e\u3059\u3002\u3059\u3079\u3066\u306e\u5358\u8a9e \u30d0\u30c4 \u79c1 {displaystyle x_ {i}} \u90e8\u5206\u7684\u306a\u5408\u8a08\u3068\u3057\u3066\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002 \u30d0\u30c4 i= \u2211 n=0i\u30d0\u30c4 i\uff08 t \uff09\uff09 t p\u3002 {displaystyle x_ {i} = sum _ {n = 0}^{i} x_ {i}\uff08t\uff09t_ {p}\u3002} \u2191 a b c  B.P. Demidowicz\u3001I.A\u3002\u30de\u30ed\u30f3\u3001 \u6570\u5024\u7684\u65b9\u6cd5 \u3001\u30d1\u30fc\u30c82\u3001PWN\u3001\u30ef\u30eb\u30b7\u30e3\u30ef1965\u3002  \u2191  B.\u30aa\u30eb\u30c4\u30a1\u30a6\u30b9\u30ad\u30fc\u3001 \u9078\u629e\u3055\u308c\u305f\u6570\u5024\u65b9\u6cd5 \u3001\u7de8\u30af\u30e9\u30af\u30fc\u5de5\u79d1\u5927\u5b66\u3001\u30af\u30e9\u30af\u30d52007\u5e74\u3002  \u2191  sh\u3002\u30df\u30b1\u30e9\u30bc\u3001 \u6570\u5b66\u7684\u306a\u30a2\u30ca\u30eb\u306e\u6570\u5024\u7684\u65b9\u6cd5 \u3001Gostehizdat\u30011953\u3001d xiii\u3001xviii\u3002       (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/1473#breadcrumbitem","name":"\u6570\u5024\u7d71\u5408 &#8211; \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2\u3001\u7121\u6599\u200b\u200b\u767e\u79d1\u4e8b\u5178"}}]}]