. . . . . . "13435"^^ . . . . . "\u89E3\u6790\u89E3"@zh . . "585143"^^ . . . "En math\u00E9matiques, une expression de forme ferm\u00E9e (\u00E9galement appel\u00E9e expression ferm\u00E9e, expression de forme close, expression close ou expression explicite) est une expression math\u00E9matique pouvant s'obtenir par une combinaison de nombres ou de fonctions et d'op\u00E9rations de r\u00E9f\u00E9rence."@fr . "V matematice se analytick\u00FDm \u0159e\u0161en\u00EDm rozum\u00ED takov\u00FD postup z\u00EDsk\u00E1n\u00ED v\u00FDsledku, kter\u00FD p\u0159ipou\u0161t\u00ED vyu\u017Eit\u00ED pouze zn\u00E1m\u00FDch vztah\u016F (rovnost\u00ED, nerovnost\u00ED) a ekvivalentn\u00EDch \u00FAprav matematick\u00FDch konstrukc\u00ED. Je-li analytick\u00FD postup obt\u00ED\u017En\u00FD (nap\u0159. z d\u016Fvodu slo\u017Eitosti n\u011Bkter\u00E9ho relevantn\u00EDho vzorce), nebo dokonce nemo\u017En\u00FD (kup\u0159. pro nedostate\u010Dnost reperto\u00E1ru rovnocenn\u00FDch \u00FAprav), lze k vy\u0159e\u0161en\u00ED \u00FAlohy pou\u017E\u00EDt numerick\u00E9 \u0159e\u0161en\u00ED."@cs . "\u0641\u064A \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0627\u062A\u060C \u062A\u0639\u0628\u064A\u0631 \u0645\u0646\u063A\u0644\u0642 \u0627\u0644\u0634\u0643\u0644 (\u0628\u0627\u0644\u0625\u0646\u062C\u0644\u064A\u0632\u064A\u0629: Closed-form expression)\u200F\u060C \u0647\u0648 \u062A\u0639\u0628\u064A\u0631 \u0631\u064A\u0627\u0636\u064A\u0627\u062A\u064A \u0639\u064F\u0628\u0631 \u0639\u0646\u0647 \u0628\u0627\u0633\u062A\u0639\u0645\u0627\u0644 \u0639\u062F\u062F \u0645\u0646\u062A\u0647 \u0645\u0646 \u0627\u0644\u0639\u0645\u0644\u064A\u0627\u062A. \u0642\u062F \u064A\u062D\u062A\u0648\u064A \u062A\u0639\u0628\u064A\u0631 \u0645\u0646\u063A\u0644\u0642 \u0627\u0644\u0634\u0643\u0644 \u0639\u0644\u0649 \u062B\u0627\u0628\u062A\u0627\u062A \u0648\u0645\u062A\u063A\u064A\u0631\u0627\u062A \u0648\u0639\u0645\u0644\u064A\u0627\u062A \u0645\u0639\u0631\u0648\u0641\u0629 (\u0645\u062B\u0644 + \u2212 \u00D7 \u00F7) \u0648\u062F\u0648\u0627\u0644 \u0645\u0646 \u0642\u0628\u064A\u0644 \u0627\u0644\u062C\u0630\u0631 \u0627\u0644\u0646\u0648\u0646\u064A \u0648\u0627\u0644\u0623\u0633 \u0648\u0627\u0644\u0644\u0648\u063A\u0627\u0631\u064A\u062A\u0645 \u0648\u0627\u0644\u062F\u0648\u0627\u0644 \u0627\u0644\u0645\u062B\u0644\u062B\u064A\u0629 \u0648\u0627\u0644\u062F\u0648\u0627\u0644 \u0627\u0644\u0632\u0627\u0626\u062F\u064A\u0629 \u0627\u0644\u0639\u0643\u0633\u064A\u0629.\u0644\u0627 \u0625\u0645\u0643\u0627\u0646\u064A\u0629 \u0644\u0648\u062C\u0648\u062F \u0646\u0647\u0627\u064A\u0627\u062A \u0623\u0648 \u0627\u0634\u062A\u0642\u0627\u0642\u0627\u062A \u0623\u0648 \u062A\u0643\u0627\u0645\u0644\u0627\u062A \u0641\u064A \u062A\u0639\u0628\u064A\u0631 \u0645\u0646\u063A\u0644\u0642 \u0627\u0644\u0634\u0643\u0644."@ar . . . "In mathematics, a closed-form expression is a mathematical expression that uses a finite number of standard operations. It may contain constants, variables, certain well-known operations (e.g., + \u2212 \u00D7 \u00F7), and functions (e.g., nth root, exponent, logarithm, trigonometric functions, and inverse hyperbolic functions), but usually no limit, differentiation, or integration. The set of operations and functions may vary with author and context."@en . . . "Wz\u00F3r jawny \u2013 wz\u00F3r matematyczny na warto\u015B\u0107 wyraz\u00F3w ci\u0105gu lub warto\u015Bci funkcji zale\u017Cny bezpo\u015Brednio od numeru wyrazu ci\u0105gu, lub argument\u00F3w funkcji. Kryteri\u00F3w wzoru jawnego nie spe\u0142niaj\u0105 np. definicje rekurencyjne ci\u0105g\u00F3w lub definicje funkcji poprzez r\u00F3wnanie funkcyjne."@pl . "Dalam matematika, Ekspresi bentuk-tertutup adalah ekspresi matematika yang diekspresikan menggunakan hingga dari operasi standar. Ini mungkin berisi konstanta, variabel, \"terkenal\" tertentu operasi (misalnya, + - \u00D7 \u00F7), dan fungsi (misalnya, akar ke- ke-', eksponen, logaritma , fungsi trigonometri, dan fungsi hiperbolik invers), tetapi biasanya tidak ada , diferensiasi, atau integrasi. Himpunan operasi dan fungsi yang diterima dalam ekspresi bentuk tertutup mungkin berbeda dengan penulis dan konteks."@in . . "\u0641\u064A \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0627\u062A\u060C \u062A\u0639\u0628\u064A\u0631 \u0645\u0646\u063A\u0644\u0642 \u0627\u0644\u0634\u0643\u0644 (\u0628\u0627\u0644\u0625\u0646\u062C\u0644\u064A\u0632\u064A\u0629: Closed-form expression)\u200F\u060C \u0647\u0648 \u062A\u0639\u0628\u064A\u0631 \u0631\u064A\u0627\u0636\u064A\u0627\u062A\u064A \u0639\u064F\u0628\u0631 \u0639\u0646\u0647 \u0628\u0627\u0633\u062A\u0639\u0645\u0627\u0644 \u0639\u062F\u062F \u0645\u0646\u062A\u0647 \u0645\u0646 \u0627\u0644\u0639\u0645\u0644\u064A\u0627\u062A. \u0642\u062F \u064A\u062D\u062A\u0648\u064A \u062A\u0639\u0628\u064A\u0631 \u0645\u0646\u063A\u0644\u0642 \u0627\u0644\u0634\u0643\u0644 \u0639\u0644\u0649 \u062B\u0627\u0628\u062A\u0627\u062A \u0648\u0645\u062A\u063A\u064A\u0631\u0627\u062A \u0648\u0639\u0645\u0644\u064A\u0627\u062A \u0645\u0639\u0631\u0648\u0641\u0629 (\u0645\u062B\u0644 + \u2212 \u00D7 \u00F7) \u0648\u062F\u0648\u0627\u0644 \u0645\u0646 \u0642\u0628\u064A\u0644 \u0627\u0644\u062C\u0630\u0631 \u0627\u0644\u0646\u0648\u0646\u064A \u0648\u0627\u0644\u0623\u0633 \u0648\u0627\u0644\u0644\u0648\u063A\u0627\u0631\u064A\u062A\u0645 \u0648\u0627\u0644\u062F\u0648\u0627\u0644 \u0627\u0644\u0645\u062B\u0644\u062B\u064A\u0629 \u0648\u0627\u0644\u062F\u0648\u0627\u0644 \u0627\u0644\u0632\u0627\u0626\u062F\u064A\u0629 \u0627\u0644\u0639\u0643\u0633\u064A\u0629.\u0644\u0627 \u0625\u0645\u0643\u0627\u0646\u064A\u0629 \u0644\u0648\u062C\u0648\u062F \u0646\u0647\u0627\u064A\u0627\u062A \u0623\u0648 \u0627\u0634\u062A\u0642\u0627\u0642\u0627\u062A \u0623\u0648 \u062A\u0643\u0627\u0645\u0644\u0627\u062A \u0641\u064A \u062A\u0639\u0628\u064A\u0631 \u0645\u0646\u063A\u0644\u0642 \u0627\u0644\u0634\u0643\u0644."@ar . . . "En math\u00E9matiques, une expression de forme ferm\u00E9e (\u00E9galement appel\u00E9e expression ferm\u00E9e, expression de forme close, expression close ou expression explicite) est une expression math\u00E9matique pouvant s'obtenir par une combinaison de nombres ou de fonctions et d'op\u00E9rations de r\u00E9f\u00E9rence. On emploie parfois le terme formule \u00E0 la place du terme expression : formule de forme ferm\u00E9e, formule explicite, formule de forme close, etc. Le plus souvent, cette terminologie s'emploie pour des solutions d'\u00E9quations ou de syst\u00E8mes d'\u00E9quations. On parlera alors plut\u00F4t de solutions de forme ferm\u00E9e, de solutions explicites, etc. Les op\u00E9rations de r\u00E9f\u00E9rence admissibles d\u00E9pendent de la nature du probl\u00E8me consid\u00E9r\u00E9 : pour un probl\u00E8me de nature arithm\u00E9tique, on pourra par exemple admettre les nombres entiers, l'addition, la soustraction, la multiplication, et l'extraction de racines ; pour un probl\u00E8me alg\u00E9brique, on ajoutera la division ; il est courant en analyse d'ajouter les fonctions exponentielle et logarithme (les fonctions trigonom\u00E9triques peuvent \u00EAtre exprim\u00E9es \u00E0 l'aide de ces deux fonctions), et plus g\u00E9n\u00E9ralement la bijection r\u00E9ciproque d'une bijection donn\u00E9e, ou encore la solution d'une \u00E9quation diff\u00E9rentielle de r\u00E9f\u00E9rence dont on se sert pour exprimer les solutions d'autres \u00E9quations diff\u00E9rentielles (on emploie dans ce domaine le terme d'expression/formule analytique)."@fr . . . . . . "In mathematics, a closed-form expression is a mathematical expression that uses a finite number of standard operations. It may contain constants, variables, certain well-known operations (e.g., + \u2212 \u00D7 \u00F7), and functions (e.g., nth root, exponent, logarithm, trigonometric functions, and inverse hyperbolic functions), but usually no limit, differentiation, or integration. The set of operations and functions may vary with author and context."@en . . . . "Es diu que una equaci\u00F3 \u00E9s una soluci\u00F3 en forma tancada si resol un problema donat en termes de funcions i operacions matem\u00E0tiques triades d'un conjunt limitat i generalment acceptat. La qualificaci\u00F3 d'una forma tancada \u00E9s una cosa arbitr\u00E0ria, ja que dep\u00E8n en gran manera del conjunt d'operacions i funcions predefinit. Per exemple, una s\u00E8rie (el sumatori de tots els termes d'una successi\u00F3 infinita) no se sol considerar forma tancada, a menys que s'inclogui en el conjunt d'operadors un operador de sumat\u00F2ria d'infinits termes d'una s\u00E8rie."@ca . . . . . . . . . . . "Forma tancada"@ca . "Closed-Form Solution"@en . . . . "\u062A\u0639\u0628\u064A\u0631 \u0645\u0646\u063A\u0644\u0642 \u0627\u0644\u0634\u0643\u0644"@ar . . . . . . . . . . . "Se dice que una ecuaci\u00F3n es una soluci\u00F3n en forma cerrada si resuelve un problema dado en t\u00E9rminos de funciones y operaciones matem\u00E1ticas elegidas de un conjunto limitado y generalmente aceptado. La calificaci\u00F3n de una forma cerrada es algo arbitraria, ya que depende en gran manera del conjunto de operaciones y funciones predefinido. Por ejemplo, una serie (la sumatoria de todos los t\u00E9rminos de una sucesi\u00F3n infinita) no se suele considerar forma cerrada; a menos que se incluya en el conjunto de operadores un operador de sumatoria de infinitos t\u00E9rminos de una serie. \n* Datos: Q777407"@es . . . . . "Wz\u00F3r jawny \u2013 wz\u00F3r matematyczny na warto\u015B\u0107 wyraz\u00F3w ci\u0105gu lub warto\u015Bci funkcji zale\u017Cny bezpo\u015Brednio od numeru wyrazu ci\u0105gu, lub argument\u00F3w funkcji. Kryteri\u00F3w wzoru jawnego nie spe\u0142niaj\u0105 np. definicje rekurencyjne ci\u0105g\u00F3w lub definicje funkcji poprzez r\u00F3wnanie funkcyjne."@pl . . . . . . . "Dalam matematika, Ekspresi bentuk-tertutup adalah ekspresi matematika yang diekspresikan menggunakan hingga dari operasi standar. Ini mungkin berisi konstanta, variabel, \"terkenal\" tertentu operasi (misalnya, + - \u00D7 \u00F7), dan fungsi (misalnya, akar ke- ke-', eksponen, logaritma , fungsi trigonometri, dan fungsi hiperbolik invers), tetapi biasanya tidak ada , diferensiasi, atau integrasi. Himpunan operasi dan fungsi yang diterima dalam ekspresi bentuk tertutup mungkin berbeda dengan penulis dan konteks."@in . . . . "Expression de forme ferm\u00E9e"@fr . . . "Ekspresi bentuk tertutup"@in . . . . . "Em matem\u00E1tica, uma express\u00E3o \u00E9 dita ser uma express\u00E3o de forma fechada se, e somente se, pode ser expressa analiticamente em termos de um n\u00FAmero delimitado de certas fun\u00E7\u00F5es bem conhecidas. Tipicamente, estas bem conhecidas fun\u00E7\u00F5es s\u00E3o definidas ser fun\u00E7\u00F5es elementares - constantes, uma vari\u00E1vel x, opera\u00E7\u00F5es elementares de aritm\u00E9tica (+ \u2013 \u00D7 \u00F7 \u2013), ra\u00EDzes n-\u00E9simas, exponenciais e logaritmos (os quais ent\u00E3o tamb\u00E9m incluem fun\u00E7\u00F5es trigonometricas e fun\u00E7\u00F5es trigonometricas inversas)."@pt . . . . . . . . "Closed-form expression"@en . "Analytick\u00E9 \u0159e\u0161en\u00ED"@cs . . . . . "Closed-FormSolution"@en . . "Wz\u00F3r jawny"@pl . . "Forma fechada (matem\u00E1tica)"@pt . . . . . "\u89E3\u6790\u89E3\uFF0C\u53C8\u7A31\u70BA\u9589\u5F0F\u89E3\uFF08\u82F1\u8A9E\uFF1AAnalytic expression\uFF09\uFF0C\u662F\u53EF\u4EE5\u7528\u89E3\u6790\u8868\u9054\u5F0F\u4F86\u8868\u9054\u7684\u89E3\u3002\u5728\u6570\u5B66\u4E0A\uFF0C\u5982\u679C\u4E00\u4E2A\u65B9\u7A0B\u6216\u8005\u65B9\u7A0B\u7EC4\u5B58\u5728\u7684\u67D0\u4E9B\u89E3\uFF0C\u662F\u7531\u6709\u9650\u6B21\u5E38\u89C1\u8FD0\u7B97\u7684\u7D44\u5408\u7ED9\u51FA\u7684\u5F62\u5F0F\uFF0C\u5219\u79F0\u8BE5\u65B9\u7A0B\u5B58\u5728\u89E3\u6790\u89E3\u3002\u4E8C\u6B21\u65B9\u7A0B\u7684\u6839\u5C31\u662F\u4E00\u4E2A\u89E3\u6790\u89E3\u7684\u5178\u578B\u4F8B\u5B50\u3002\u5728\u4F4E\u5E74\u7EA7\u6570\u5B66\u7684\u6559\u5B66\u5F53\u4E2D\uFF0C\u89E3\u6790\u89E3\u4E5F\u88AB\u79F0\u4E3A\u516C\u5F0F\u89E3\u3002 \u5F53\u89E3\u6790\u89E3\u4E0D\u5B58\u5728\u65F6\uFF0C\u6BD4\u5982\u4E94\u6B21\u4EE5\u53CA\u66F4\u9AD8\u6B21\u7684\u4EE3\u6570\u65B9\u7A0B\uFF0C\u5219\u8BE5\u65B9\u7A0B\u53EA\u80FD\u7528\u6570\u503C\u5206\u6790\u7684\u65B9\u6CD5\u6C42\u89E3\u8FD1\u4F3C\u503C\u3002\u5927\u591A\u6578\u504F\u5FAE\u5206\u65B9\u7A0B\uFF0C\u5C24\u5176\u662F\u975E\u7EBF\u6027\u504F\u5FAE\u5206\u65B9\u7A0B\uFF0C\u90FD\u53EA\u6709\u6578\u503C\u89E3\u3002 \u89E3\u6790\u8868\u9054\u5F0F\u7684\u51C6\u786E\u542B\u4E49\u4F9D\u8D56\u4E8E\u4F55\u79CD\u8FD0\u7B97\u79F0\u4E3A\u5E38\u89C1\u8FD0\u7B97\u6216\u5E38\u89C1\u51FD\u6570\u3002\u4F20\u7EDF\u4E0A\uFF0C\u53EA\u6709\u521D\u7B49\u51FD\u6570\u88AB\u770B\u4F5C\u5E38\u89C1\u51FD\u6570\uFF0C\u65E0\u7A77\u7EA7\u6570\u3001\u5E8F\u5217\u7684\u6781\u9650\u3001\u8FDE\u5206\u6570\u7B49\u90FD\u4E0D\u88AB\u770B\u4F5C\u5E38\u89C1\u51FD\u6570\u3002\u6309\u8FD9\u79CD\u5B9A\u4E49\uFF0C\u8BB8\u591A\u7D2F\u79EF\u5206\u5E03\u51FD\u6570\u65E0\u6CD5\u5199\u6210\u89E3\u6790\u8868\u9054\u5F0F\u3002\u4F46\u5982\u679C\u628A\u7279\u6B8A\u51FD\u6570\uFF0C\u6BD4\u5982\u8BEF\u5DEE\u51FD\u6570\u6216gamma\u51FD\u6570\u4E5F\u770B\u4F5C\u5E38\u89C1\u51FD\u6570\uFF0C\u5219\u7D2F\u79EF\u5206\u5E03\u51FD\u6570\u53EF\u4EE5\u5199\u6210\u89E3\u6790\u8868\u9054\u5F0F\u3002 \u5728\u8BA1\u7B97\u673A\u5E94\u7528\u4E2D\uFF0C\u8FD9\u4E9B\u7279\u6B8A\u51FD\u6570\u56E0\u4E3A\u5927\u591A\u6709\u73B0\u6210\u7684\u6570\u503C\u6CD5\u5B9E\u73B0\uFF0C\u5B83\u4EEC\u901A\u5E38\u88AB\u770B\u4F5C\u5E38\u89C1\u8FD0\u7B97\u6216\u5E38\u89C1\u51FD\u6570\u3002\u5B9E\u9645\u4E0A\uFF0C\u5728\u8BA1\u7B97\u673A\u7684\u8BA1\u7B97\u8FC7\u7A0B\u4E2D\uFF0C\u591A\u6570\u57FA\u672C\u51FD\u6570\u90FD\u662F\u7528\u6570\u503C\u6CD5\u8BA1\u7B97\u7684\uFF0C\u6240\u4EE5\u6240\u8C13\u7684\u57FA\u672C\u51FD\u6570\u548C\u7279\u6B8A\u51FD\u6570\u5BF9\u8BA1\u7B97\u673A\u800C\u8A00\u5E76\u65E0\u533A\u522B\u3002"@zh . . "Es diu que una equaci\u00F3 \u00E9s una soluci\u00F3 en forma tancada si resol un problema donat en termes de funcions i operacions matem\u00E0tiques triades d'un conjunt limitat i generalment acceptat. La qualificaci\u00F3 d'una forma tancada \u00E9s una cosa arbitr\u00E0ria, ja que dep\u00E8n en gran manera del conjunt d'operacions i funcions predefinit. Per exemple, una s\u00E8rie (el sumatori de tots els termes d'una successi\u00F3 infinita) no se sol considerar forma tancada, a menys que s'inclogui en el conjunt d'operadors un operador de sumat\u00F2ria d'infinits termes d'una s\u00E8rie. Hom diu que un problema \u00E9s tractable si es pot resoldre en termes d'una expressi\u00F3 en forma tancada."@ca . . . . "Em matem\u00E1tica, uma express\u00E3o \u00E9 dita ser uma express\u00E3o de forma fechada se, e somente se, pode ser expressa analiticamente em termos de um n\u00FAmero delimitado de certas fun\u00E7\u00F5es bem conhecidas. Tipicamente, estas bem conhecidas fun\u00E7\u00F5es s\u00E3o definidas ser fun\u00E7\u00F5es elementares - constantes, uma vari\u00E1vel x, opera\u00E7\u00F5es elementares de aritm\u00E9tica (+ \u2013 \u00D7 \u00F7 \u2013), ra\u00EDzes n-\u00E9simas, exponenciais e logaritmos (os quais ent\u00E3o tamb\u00E9m incluem fun\u00E7\u00F5es trigonometricas e fun\u00E7\u00F5es trigonometricas inversas)."@pt . . . . . . . . "V matematice se analytick\u00FDm \u0159e\u0161en\u00EDm rozum\u00ED takov\u00FD postup z\u00EDsk\u00E1n\u00ED v\u00FDsledku, kter\u00FD p\u0159ipou\u0161t\u00ED vyu\u017Eit\u00ED pouze zn\u00E1m\u00FDch vztah\u016F (rovnost\u00ED, nerovnost\u00ED) a ekvivalentn\u00EDch \u00FAprav matematick\u00FDch konstrukc\u00ED. Je-li analytick\u00FD postup obt\u00ED\u017En\u00FD (nap\u0159. z d\u016Fvodu slo\u017Eitosti n\u011Bkter\u00E9ho relevantn\u00EDho vzorce), nebo dokonce nemo\u017En\u00FD (kup\u0159. pro nedostate\u010Dnost reperto\u00E1ru rovnocenn\u00FDch \u00FAprav), lze k vy\u0159e\u0161en\u00ED \u00FAlohy pou\u017E\u00EDt numerick\u00E9 \u0159e\u0161en\u00ED."@cs . . . . . . . . . "Se dice que una ecuaci\u00F3n es una soluci\u00F3n en forma cerrada si resuelve un problema dado en t\u00E9rminos de funciones y operaciones matem\u00E1ticas elegidas de un conjunto limitado y generalmente aceptado. La calificaci\u00F3n de una forma cerrada es algo arbitraria, ya que depende en gran manera del conjunto de operaciones y funciones predefinido. Por ejemplo, una serie (la sumatoria de todos los t\u00E9rminos de una sucesi\u00F3n infinita) no se suele considerar forma cerrada; a menos que se incluya en el conjunto de operadores un operador de sumatoria de infinitos t\u00E9rminos de una serie. \n* Datos: Q777407"@es . . . . "Forma cerrada (matem\u00E1tica)"@es . "1122803483"^^ . . . . . . . . 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