[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/19930#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/19930","headline":"Langevin Function-Wikipedia","name":"Langevin Function-Wikipedia","description":"before-content-x4 \u30e9\u30f3\u30b8\u30e5\u30d3\u30f3\u95a2\u6570 l \uff08 \u30d0\u30c4 \uff09\uff09 {displaystyle l\uff08x\uff09} after-content-x4 \uff08\u7269\u7406\u5b66\u8005\u306b\u3088\u308b\u3068\u3001\u30dd\u30fc\u30eb\u30fb\u30e9\u30f3\u30b2\u30d3\u30f3\uff081872\u20131946\uff09\uff09\uff09\u306f\u3001\u65b9\u5411\u504f\u5149\u3001\u504f\u5149\u3001\u78c1\u5316\u3001\u62b5\u6297\u3092\u8a08\u7b97\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u308b\u6570\u5b66\u7684\u6a5f\u80fd\u3067\u3059\u3002 \u30e9\u30f3\u30b8\u30e5\u30d3\u30f3\u95a2\u6570 [\u521d\u3081] \u3067\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u307e\u3059 after-content-x4 l \uff08 \u30d0\u30c4 \uff09\uff09 = coth","datePublished":"2023-05-02","dateModified":"2023-05-02","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/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\/thumb\/c\/c5\/Mplwp_Langevin-function.svg\/220px-Mplwp_Langevin-function.svg.png","url":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/c\/c5\/Mplwp_Langevin-function.svg\/220px-Mplwp_Langevin-function.svg.png","height":"147","width":"220"},"url":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/19930","wordCount":4539,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4  \u30e9\u30f3\u30b8\u30e5\u30d3\u30f3\u95a2\u6570  l \uff08 \u30d0\u30c4 \uff09\uff09 {displaystyle l\uff08x\uff09}        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\uff08\u7269\u7406\u5b66\u8005\u306b\u3088\u308b\u3068\u3001\u30dd\u30fc\u30eb\u30fb\u30e9\u30f3\u30b2\u30d3\u30f3\uff081872\u20131946\uff09\uff09\uff09\u306f\u3001\u65b9\u5411\u504f\u5149\u3001\u504f\u5149\u3001\u78c1\u5316\u3001\u62b5\u6297\u3092\u8a08\u7b97\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u308b\u6570\u5b66\u7684\u6a5f\u80fd\u3067\u3059\u3002 \u30e9\u30f3\u30b8\u30e5\u30d3\u30f3\u95a2\u6570 [\u521d\u3081] \u3067\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u307e\u3059        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4l \uff08 \u30d0\u30c4 \uff09\uff09 = coth \u2061 \uff08 \u30d0\u30c4 \uff09\uff09  –  1x{displaystyle l\uff08x\uff09= coth\uff08x\uff09 –  {1 over x}}} \u3001 \u3057\u305f\u304c\u3063\u3066 coth {displaystyle coth} Kotangen Hyperbolicus\u3092\u793a\u3057\u307e\u3057\u305f\u3002 \u6700\u3082\u3088\u304f\u77e5\u3089\u308c\u3066\u3044\u308b\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u306f\u3001\u5916\u5074\u306e\u78c1\u5834\u306e\u5e38\u78c1\u77f3\u306e\u534a\u30af\u30e9\u30b7\u30c3\u30af\u306a\u8aac\u660e\u3067\u3059\u3002\u3053\u306e\u76ee\u7684\u306e\u305f\u3081\u306b\u3001Longvin\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc \u30d0\u30c4 {displaystyle xi} \u7d39\u4ecb\u3055\u308c\u305f\uff1a        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u30d0\u30c4 = mBkBT{displaystyle xi = {frac {mb} {k_ {mathrm {b}} t}}}} \u500b\u3005\u306e\u30d5\u30a9\u30fc\u30df\u30e5\u30e9\u30b5\u30a4\u30f3\u306f\u3001\u6b21\u306e\u30b5\u30a4\u30ba\u3092\u8868\u3057\u307e\u3059\u3002 \u78c1\u5316\u7528 m {displaystyle m} \u305d\u306e\u5f8c\u3001\u4e00\u822c\u7684\u306a\u7d50\u679c\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002 m = n m l \uff08 \u30d0\u30c4 \uff09\uff09 {displaystyle m = nml\uff08xi\uff09} n {displaystyle n} \u751f\u5730\u306e\u91cf\u3092\u8868\u3057\u307e\u3059 m {displaystyle m} \u5e38\u78c1\u6027\u306e\u500b\u3005\u306e\u30b9\u30d4\u30f3\u306e\u78c1\u6c17\u30e2\u30fc\u30e1\u30f3\u30c8\u306e\u305f\u3081\u306b\u3002\u5e38\u78c1\u6027\u306e\u5225\u306e\u91cf\u5b50\u6a5f\u68b0\u7684\u8aac\u660e\u306f\u3001\u30d6\u30ea\u30eb\u30a2\u30f3\u95a2\u6570\u306b\u3088\u3063\u3066\u4e0e\u3048\u3089\u308c\u307e\u3059\u3002 \u3059\u3079\u3066\u306e\u5b9f\u969b\u306e\u5024x\u53ce\u675f\u306b\u3064\u3044\u3066\u3001\u3053\u306e\u5408\u8a08\u306e\u5217\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002 l \uff08 \u30d0\u30c4 \uff09\uff09 = \u2211n=1\u221e2x\u03c02n2+x2{displaystyle l\uff08x\uff09= sum _ {n = 1}^{infty} {frac {2x} {pi^{2} n^{2}+x^{2}}}}}}}} \u305f\u3068\u3048\u3070\u3001\u305d\u308c\u306f\u3001\u305d\u306e\u5217\u306e\u5217\u306e\u500b\u5225\u306e\u30b3\u30fc\u30b7\u30fc\u5206\u5e03\u306b\u9069\u7528\u3055\u308c\u307e\u3059\u3002 \u2211n=1\u221e1n2+1= \u03c0L(\u03c0)2{displaystyle sum _ {n = 1}^{infty} {frac {1} {n^{2} +1}} = {frac {pi l\uff08pi\uff09}}}}}}}}}}} \u3057\u305f\u304c\u3063\u3066\u3001\u6b63\u65b9\u5f62\u6570\u306e\u5f8c\u7d99\u8005\u306e\u629c\u672c\u7684\u306a\u5024\u306e\u7121\u9650\u306e\u5408\u8a08\u306f\u57fa\u672c\u7684\u3067\u3059\u3002 \u305d\u3057\u3066\u3001\u6b21\u306e\u5236\u9650\u304c\u9069\u7528\u3055\u308c\u307e\u3059\uff1a z \uff08 2 \uff09\uff09 = \u2211n=1\u221e1n2= limx\u21920\u2211n=1\u221e1n2+x2= limx\u21920\u03c0L(\u03c0x)2x= \u03c026{displaystyle zeta\uff082\uff09= sum _ {n = 1}^{infty} {frac {1} {n^{2}}} = lim _ {xRightArrow 0} sum _ {n = 1}^{infty} {frac {1} {n^{2} {2} {2}+x^{2} {2} {2} {2} {2} {2} {2}+ } {frac {pi l\uff08pi x\uff09} {2x}} = {frac {pi ^{2}} {6}}}} \u3053\u306e\u5024\u306f\u3001SO -Caleded Basel\u554f\u984c\u306e\u89e3\u6c7a\u7b56\u3067\u3059\u3002 Maclaurin\u30b7\u30ea\u30fc\u30ba\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002 l \uff08 \u30d0\u30c4 \uff09\uff09 = \u2211n=1\u221e2 \uff08  –  \u521d\u3081 )n+1\u03c0\u22122nz \uff08 2 n \uff09\uff09 x2n\u22121= 13\u30d0\u30c4  –  145x3+ 2945x5 –  14725x7+ \u22ef {displaystyle l\uff08x\uff09= sum _ {n = 1}^{infty} 2\uff08-1\uff09^{n+1} pi^{-2n} zeta\uff082n\uff09x^{2n-1} = {frac {1} {3}}} x- {45} {45} {{45} {{45}} {45} {45} {45} {45} {45} {45} {45} {45} {45} {45} {45} 45}} x^{5}  –  {frac {1} {4725}} x^{7}+cdots} \u3053\u306e\u30b7\u30ea\u30fc\u30ba\u306e\u53ce\u675f\u534a\u5f84\u306f\u3001\u5186\u03c0\u306e\u6570\u3067\u3059\u3002 \u305d\u3057\u3066\u3001\u30e9\u30f3\u30b8\u30e5\u30d3\u30f3\u95a2\u6570\u306e\u6b63\u65b9\u5f62\u306e\u305f\u3081\u306b\uff1a l \uff08 \u30d0\u30c4 )2= \u2211n=1\u221e\uff08 4 n + 6 \uff09\uff09 \uff08  –  \u521d\u3081 )n+1\u03c0\u22122n\u22122z \uff08 2 n + 2 \uff09\uff09 x2n= 19x2 –  2135x4+ 1525x6 –  28505x8+ \u22ef {displaystyle l\uff08x\uff09^{2} = sum _ {n = 1}^{infty}\uff084n+6\uff09\uff08 –  1\uff09^{n+1} pi^{-2n-2} Zeta\uff082n+2\uff09x^{2n} = {frac {1} {{{{{{{{{{{{{{{{{{{{{{{{{}}}}}}}}}}}}}}}}}}}} {{{} {{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{}\uff09\uff09 ^{4}+{frac {1} {525}} x^{6}  –  {frac {2} {8505}} x^{8}+cdots} \u30ae\u30ea\u30b7\u30e3\u6587\u5b57\u30bc\u30fc\u30bf\u306f\u3001\u30ea\u30fc\u30de\u30f3\u30bc\u30fc\u30bf\u95a2\u6570\u3092\u8868\u3057\u3066\u3044\u307e\u3059\u3002 \u8fd1\u4f3c [\u521d\u3081] \u306e\u30ed\u30f3\u30b0\u30d3\u30f3\u95a2\u6570 | \u30d0\u30c4 | \u226a \u521d\u3081 {displaystyle | x | ll 1} \u306f l \uff08 \u30d0\u30c4 \uff09\uff09 = coth \u2061 \uff08 \u30d0\u30c4 \uff09\uff09  –  1x\u2248 x3{displaystyle l\uff08x\uff09= coth\uff08x\uff09 –  {frac {1} {x}} compx {frac {x} {3}}} \u3002 \u305f\u3081\u306b \u30d0\u30c4 \u226b \u521d\u3081 {displaystyle xgg 1} \u8fd1\u4f3c\u304c\u9069\u7528\u3055\u308c\u307e\u3059 [\u521d\u3081] l \uff08 \u30d0\u30c4 \uff09\uff09 \u2248 \u521d\u3081  –  1x{displaystyle l\uff08x\uff09\u7d041- {frac {1} {x}}} \u3002 Langevin\u95a2\u6570\u306b\u306f\u9589\u3058\u305f\u53cd\u8ee2\u95a2\u6570\u304c\u306a\u3044\u305f\u3081\u3001\u3055\u307e\u3056\u307e\u306a\u8fd1\u4f3c\u304c\u3042\u308a\u307e\u3059\u3002\u5012\u7acb\u30e9\u30f3\u30b2\u30d3\u30f3\u95a2\u6570\u306f\u3001L\u306e\u5f8c\u308d\u306e\u6307\u6570\u4f4d\u7f6e\u306b\u5c16\u3063\u305f\u30af\u30ea\u30c3\u30d7\u306e1\u3064\u3092\u30de\u30a4\u30ca\u30b9\u3057\u3066\u793a\u3055\u308c\u3066\u3044\u307e\u3059\u3002 Lambertsche W\u6a5f\u80fd\u3068\u540c\u69d8\u306b\u3001\u3053\u306e\u9006\u8ee2\u95a2\u6570\u306f\u521d\u7b49\u306b\u306f\u8868\u793a\u3067\u304d\u307e\u305b\u3093\u3002 \u9593\u9694\u3067\u306e\u4e00\u822c\u7684\u306a\u8fd1\u4f3c \uff08  –  \u521d\u3081 \u3001 \u521d\u3081 \uff09\uff09 {displaystyle\uff08-1,1\uff09} Applies\u306fA. Cohen\u306b\u3088\u3063\u3066\u516c\u958b\u3055\u308c\u307e\u3057\u305f\uff1a [2] L\u27e8\u22121\u27e9\uff08 \u30d0\u30c4 \uff09\uff09 \u2248 \u30d0\u30c4 3\u2212x21\u2212x2{displaystyle l^{langle -1rangle}\uff08x\uff09artx x {frac {3-x^{2}} {1-x^{2}}}}}} \u3053\u306e\u8fd1\u4f3c\u306e\u6700\u5927\u306e\u76f8\u5bfe\u7684\u306a\u9593\u9055\u3044\u306f4.9\uff05\u3067\u3059 | \u30d0\u30c4 | = 0 \u3001 8 {displaystyle | x | = 0 {\u3001} 8} \u3002\u76f8\u5bfe\u7684\u306a\u30a8\u30e9\u30fc\u304c\u306f\u308b\u304b\u306b\u5c11\u306a\u3044\u4ed6\u306e\u8fd1\u4f3c\u304c\u3042\u308a\u307e\u3059\u3002 [3] [4] \u5012\u7acb\u30e9\u30f3\u30b2\u30d3\u30f3\u95a2\u6570\u306e\u30de\u30af\u30e9\u30a6\u30ea\u30f3\u30b7\u30ea\u30fc\u30ba\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059 [5] \u53ce\u675f\u534a\u5f841\u3092\u6301\u3063\u3066\u3044\u307e\u3059\uff1a L\u27e8\u22121\u27e9\uff08 \u30d0\u30c4 \uff09\uff09 \u2248 3 \u30d0\u30c4 + 95x3+ 297175x5+ 1539875x7+ \u22ef {displaystyle l^{langle -1rangle}\uff08x\uff09\u7d043x+{frac {9} {5}} x^{3}+{frac {297} {175}} x^{5}+{frac {1539}} {875} {7} {7} { \u2191 a b c  Siegmund Brandt\uff1a Elektrodynamik \u3002 Springer\u3001Berlin 2005\u3001ISBN 3-540-21458-5\u3001 S.  293 \u3002   \u2191  A.\u30b3\u30fc\u30a8\u30f3\uff1a \u9006\u30e9\u30f3\u30b8\u30e5\u30d3\u30f3\u95a2\u6570\u306b\u8fd1\u3044\u30d1\u30c7 \u3002\u306e\uff1a Rheologica Acta \u3002 30\u5e74\u3001 \u3044\u3044\u3048\u3002  3 \u30011991\u5e74\u3001 S.  270\u2013273 \u3001doi\uff1a 10.1007\/BF00366640 \u3002   \u2191  R. Jedynak\uff1a \u9006\u30e9\u30f3\u30b8\u30e5\u30d3\u30f3\u95a2\u6570\u306e\u8fd1\u4f3c\u306b\u95a2\u3059\u308b\u65b0\u3057\u3044\u4e8b\u5b9f \u3002\u306e\uff1a \u30b8\u30e3\u30fc\u30ca\u30eb\u30aa\u30d6\u30cb\u30e5\u30fc\u30c8\u30cb\u30a2\u30f3\u6d41\u4f53\u529b\u5b66 \u3002 249\u5e74\u30012017\u5e74 S.  8\u201325 \u3001doi\uff1a 10.1016 \/ j.jnnfm.2017.09.003 \u3002   \u2191  M.\u30af\u30ec\u30ac\u30fc\uff1a \u5f37\u529b\u306a\u30dd\u30ea\u30de\u30fc\u306e\u5909\u5f62\u3068\u6d41\u91cf\u306b\u95a2\u9023\u3059\u308b\u3001\u9006\u30e9\u30f3\u30b8\u30e5\u30d3\u30f3\u304a\u3088\u3073\u30d6\u30ea\u30eb\u30a2\u30f3\u6a5f\u80fd\u306e\u30b7\u30f3\u30d7\u30eb\u3067\u8a31\u5bb9\u53ef\u80fd\u306a\u3001\u6b63\u78ba\u306a\u8fd1\u4f3c\u5024 \u3002\u306e\uff1a \u30b8\u30e3\u30fc\u30ca\u30eb\u30aa\u30d6\u30cb\u30e5\u30fc\u30c8\u30cb\u30a2\u30f3\u6d41\u4f53\u529b\u5b66 \u3002 223\u5e74\u30012015\u5e74 S.  77\u201387 \u3001doi\uff1a 10.1016 \/ j.jnnfm.2015.05.007 \u3002   \u2191  https:\/\/bookks.google.de\/books\uff1fdpdwyssscfccc\uff06pg = pa277\uff06lpg = pa277\uff06dq = 9+5+25+175+1539+875\uff06source = bl\uff06ots = sav24x3u6f\uff06sig = acfu3u1qzg51x51x51x51x4jhh4h4h4h4h4h4h4h4h4h4h4h4h4h4h4h4h4h4h4h4h4h4h4h4h4h4h4 VED = 2AHUKEWICG7367EX2AHXGNAQKHAM3DWAQ6AF6BAGDEAM\uff03V = ONEPAGE\uff06Q = 9\uff05205\uff0520297\uff0520175\uff05201539\uff0520875\uff06f = false        (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\/wiki11\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/19930#breadcrumbitem","name":"Langevin Function-Wikipedia"}}]}]