<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Thomas_Bayes> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/ontology/abstract>	"\u53F2\u7279\u9748\u516C\u5F0F\uFF08Stirling's formula\uFF09\u662F\u4E00\u689D\u7528\u4F86\u53D6n\u968E\u4E58\u8FD1\u4F3C\u503C\u7684\u6578\u5B78\u516C\u5F0F\u3002\u4E00\u822C\u4F86\u8AAA\uFF0C\u7576n\u5F88\u5927\u7684\u6642\u5019\uFF0Cn\u968E\u4E58\u7684\u8A08\u7B97\u91CF\u5341\u5206\u5927\uFF0C\u6240\u4EE5\u53F2\u7279\u9748\u516C\u5F0F\u5341\u5206\u597D\u7528\uFF0C\u800C\u4E14\uFF0C\u5373\u4F7F\u5728n\u5F88\u5C0F\u7684\u6642\u5019\uFF0C\u53F2\u7279\u9748\u516C\u5F0F\u7684\u53D6\u503C\u5DF2\u7D93\u5341\u5206\u6E96\u78BA\u3002\u9019\u500B\u516C\u5F0F\u4EE5\u7684\u540D\u5B57\u547D\u540D\uFF0C\u96D6\u7136\u4E9E\u4F2F\u62C9\u7F55\u00B7\u68E3\u7F8E\u5F17\u65E9\u65BC\u53F2\u7279\u9748\u63D0\u51FA\u4E86\u4E00\u500B\u985E\u4F3C\u7684\u516C\u5F0F\uFF0C\u4F46\u7D50\u679C\u8F03\u4E0D\u7CBE\u78BA\u3002 \u53F2\u7279\u9748\u516C\u5F0F\u4E3A\uFF1A \u8FD9\u5C31\u662F\u8BF4\uFF0C\u5BF9\u4E8E\u8DB3\u591F\u5927\u7684\u6574\u6570n\uFF0C\u8FD9\u4E24\u4E2A\u6570\u4E92\u4E3A\u8FD1\u4F3C\u503C\u3002\u66F4\u52A0\u7CBE\u786E\u5730\uFF1A \u6216"@zh .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Approximation_error> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2002/07/owl#sameAs>	<http://mn.dbpedia.org/resource/\u0421\u0442\u0438\u0440\u043B\u0438\u043D\u0433\u0438\u0439\u043D_\u0442\u043E\u043C\u044A\u0451\u043E> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Srinivasa_Ramanujan> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2000/01/rdf-schema#comment>	"Matematikaren alorrean, Stirlingen hurbilketa edo Stirlingen formula deritzona, faktorialak hurbiltzeko erabiltzen den formula bat da. Beste era batera esanda, zenbaki altuen faktoriala kalkulatzea ez da batere erraza eta formula honek balio altu horretatik oso hurbil dagoen zenbaki bat itzultzen du. Hurbilketa hau oso zehatza eta erabilgarria da balio handiko zenbakien faktoriala lortzeko edota adierazpen bat beste adierazpen hurbil batera murrizteko. James Stirling, XVIII. mendeko matematikari eskoziarrari esker, n infinitura doanean ondoko limitea dugu:"@eu .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/ontology/abstract>	"\uC218\uD559\uC5D0\uC11C \uC2A4\uD138\uB9C1 \uADFC\uC0AC(\uC601\uC5B4: Stirling\u2019s approximation) \uB610\uB294 \uC2A4\uD138\uB9C1 \uACF5\uC2DD(\uC601\uC5B4: Stirling\u2019s formula)\uC740 \uD070 \uACC4\uC2B9\uC744 \uAD6C\uD558\uB294 \uADFC\uC0AC\uBC95\uC774\uB2E4."@ko .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2000/01/rdf-schema#comment>	"Em matem\u00E1tica, a f\u00F3rmula de Stirling ou aproxima\u00E7\u00E3o de Stirling \u00E9 uma f\u00F3rmula que estabelece uma aproxima\u00E7\u00E3o assint\u00F3tica ao fatorial de um n\u00FAmero. Recebe o nome do matem\u00E1tico James Stirling. Na sua forma mais conhecida, a f\u00F3rmula escreve-se: , onde \u00E9 o n\u00FAmero de Euler, tal que O que \u00E9 uma nota\u00E7\u00E3o para o limite: . A f\u00F3rmula de Stirling \u00E9 apresentada tamb\u00E9m de outra forma, comummente utilizada em aplica\u00E7\u00F5es na f\u00EDsica, por exemplo. Quando , o logaritmo natural de um fatorial \u00E9 dado por:"@pt .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/File:Stirling_error_vs_number_of_terms.svg> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/1999/02/22-rdf-syntax-ns#type>	<http://dbpedia.org/class/yago/Thinking105770926> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/property/wikiPageUsesTemplate>	<http://dbpedia.org/resource/Template:Calculus_topics> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2002/07/owl#sameAs>	<http://vi.dbpedia.org/resource/X\u1EA5p_x\u1EC9_Stirling> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2000/01/rdf-schema#comment>	"La formule de Stirling, du nom du math\u00E9maticien \u00E9cossais James Stirling, donne un \u00E9quivalent de la factorielle d'un entier naturel n quand n tend vers l'infini : que l'on trouve souvent \u00E9crite ainsi : o\u00F9 le nombre e d\u00E9signe la base de l'exponentielle."@fr .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2000/01/rdf-schema#label>	"F\u00F3rmula de Stirling"@es .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2002/07/owl#sameAs>	<http://el.dbpedia.org/resource/\u03A4\u03CD\u03C0\u03BF\u03C2_\u03A3\u03C4\u03AF\u03C1\u03BB\u03B9\u03BD\u03B3\u03BA> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2000/01/rdf-schema#label>	"\u062A\u0642\u0631\u064A\u0628 \u0633\u062A\u064A\u0631\u0644\u064A\u0646\u063A"@ar .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2002/07/owl#sameAs>	<http://www.wikidata.org/entity/Q470877> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Asymptotic_analysis> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2002/07/owl#sameAs>	<http://ca.dbpedia.org/resource/F\u00F3rmula_de_Stirling> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2002/07/owl#sameAs>	<http://hu.dbpedia.org/resource/Stirling-formula> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2000/01/rdf-schema#label>	"Formule van Stirling"@nl .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Euler\u2013Maclaurin_formula> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/ontology/wikiPageExternalLink>	<http://www.luschny.de/math/factorial/approx/SimpleCases.html> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/John_Canton> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/property/wikiPageUsesTemplate>	<http://dbpedia.org/resource/Template:=> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Pochhammer_symbol> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://purl.org/dc/terms/subject>	<http://dbpedia.org/resource/Category:Analytic_number_theory> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2000/01/rdf-schema#comment>	"\u53F2\u7279\u9748\u516C\u5F0F\uFF08Stirling's formula\uFF09\u662F\u4E00\u689D\u7528\u4F86\u53D6n\u968E\u4E58\u8FD1\u4F3C\u503C\u7684\u6578\u5B78\u516C\u5F0F\u3002\u4E00\u822C\u4F86\u8AAA\uFF0C\u7576n\u5F88\u5927\u7684\u6642\u5019\uFF0Cn\u968E\u4E58\u7684\u8A08\u7B97\u91CF\u5341\u5206\u5927\uFF0C\u6240\u4EE5\u53F2\u7279\u9748\u516C\u5F0F\u5341\u5206\u597D\u7528\uFF0C\u800C\u4E14\uFF0C\u5373\u4F7F\u5728n\u5F88\u5C0F\u7684\u6642\u5019\uFF0C\u53F2\u7279\u9748\u516C\u5F0F\u7684\u53D6\u503C\u5DF2\u7D93\u5341\u5206\u6E96\u78BA\u3002\u9019\u500B\u516C\u5F0F\u4EE5\u7684\u540D\u5B57\u547D\u540D\uFF0C\u96D6\u7136\u4E9E\u4F2F\u62C9\u7F55\u00B7\u68E3\u7F8E\u5F17\u65E9\u65BC\u53F2\u7279\u9748\u63D0\u51FA\u4E86\u4E00\u500B\u985E\u4F3C\u7684\u516C\u5F0F\uFF0C\u4F46\u7D50\u679C\u8F03\u4E0D\u7CBE\u78BA\u3002 \u53F2\u7279\u9748\u516C\u5F0F\u4E3A\uFF1A \u8FD9\u5C31\u662F\u8BF4\uFF0C\u5BF9\u4E8E\u8DB3\u591F\u5927\u7684\u6574\u6570n\uFF0C\u8FD9\u4E24\u4E2A\u6570\u4E92\u4E3A\u8FD1\u4F3C\u503C\u3002\u66F4\u52A0\u7CBE\u786E\u5730\uFF1A \u6216"@zh .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2000/01/rdf-schema#comment>	"\u0641\u064A \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0627\u062A\u060C \u062A\u0642\u0631\u064A\u0628 \u0633\u062A\u064A\u0631\u0644\u064A\u0646\u063A (\u0628\u0627\u0644\u0625\u0646\u062C\u0644\u064A\u0632\u064A\u0629: Stirling's approximation)\u200F (\u0623\u0648 \u0635\u064A\u063A\u0629 \u0633\u062A\u064A\u0631\u0644\u064A\u0646\u063A (\u0628\u0627\u0644\u0625\u0646\u062C\u0644\u064A\u0632\u064A\u0629: Stirling's formula)\u200F) \u0647\u0648 \u0635\u064A\u063A\u0629 \u0631\u064A\u0627\u0636\u064A\u0629 \u062A\u0633\u062A\u062E\u062F\u0645 \u0644\u062A\u0642\u0631\u064A\u0628 \u0642\u064A\u0645 \u0627\u0644\u0639\u0627\u0645\u0644\u064A \u0627\u0644\u0643\u0628\u064A\u0631\u0629. \u0633\u0645\u064A \u0643\u0630\u0644\u0643 \u0646\u0633\u0628\u0629 \u0625\u0644\u0649 \u0639\u0627\u0644\u0645 \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0627\u062A \u062C\u064A\u0645\u0633 \u0633\u062A\u064A\u0631\u0644\u064A\u0646\u063A."@ar .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Category:Analytic_number_theory> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2000/01/rdf-schema#comment>	"\u30B9\u30BF\u30FC\u30EA\u30F3\u30B0\u306E\u8FD1\u4F3C\uFF08\u82F1: Stirling's approximation\uFF09\u307E\u305F\u306F\u30B9\u30BF\u30FC\u30EA\u30F3\u30B0\u306E\u516C\u5F0F\uFF08\u82F1: Stirling's formula\uFF09\u306F\u3001\u968E\u4E57\u3001\u3042\u308B\u3044\u306F\u305D\u306E\u62E1\u5F35\u306E\u4E00\u3064\u3067\u3042\u308B\u30AC\u30F3\u30DE\u95A2\u6570\u306E\u3067\u3042\u308B\u3002\u540D\u79F0\u306F\u6570\u5B66\u8005\u306B\u3061\u306A\u3080\u3002"@ja .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/ontology/thumbnail>	<http://commons.wikimedia.org/wiki/Special:FilePath/Mplwp_factorial_gamma_stirling.svg?width=300> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/ontology/abstract>	"\u0412 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0435 \u0444\u043E\u0440\u043C\u0443\u043B\u0430 \u0421\u0442\u0438\u0440\u043B\u0438\u043D\u0433\u0430 (\u0442\u0430\u043A\u0436\u0435 \u0444\u043E\u0440\u043C\u0443\u043B\u0430 \u041C\u0443\u0430\u0432\u0440\u0430 \u2014 \u0421\u0442\u0438\u0440\u043B\u0438\u043D\u0433\u0430) \u2014 \u0444\u043E\u0440\u043C\u0443\u043B\u0430 \u0434\u043B\u044F \u043F\u0440\u0438\u0431\u043B\u0438\u0436\u0451\u043D\u043D\u043E\u0433\u043E \u0432\u044B\u0447\u0438\u0441\u043B\u0435\u043D\u0438\u044F \u0444\u0430\u043A\u0442\u043E\u0440\u0438\u0430\u043B\u0430 \u0438 \u0433\u0430\u043C\u043C\u0430-\u0444\u0443\u043D\u043A\u0446\u0438\u0438. \u041D\u0430\u0437\u0432\u0430\u043D\u0430 \u0432 \u0447\u0435\u0441\u0442\u044C \u0414\u0436\u0435\u0439\u043C\u0441\u0430 \u0421\u0442\u0438\u0440\u043B\u0438\u043D\u0433\u0430 \u0438 \u0410\u0431\u0440\u0430\u0445\u0430\u043C\u0430 \u0434\u0435 \u041C\u0443\u0430\u0432\u0440\u0430, \u043F\u043E\u0441\u043B\u0435\u0434\u043D\u0438\u0439 \u0441\u0447\u0438\u0442\u0430\u0435\u0442\u0441\u044F \u0430\u0432\u0442\u043E\u0440\u043E\u043C \u0444\u043E\u0440\u043C\u0443\u043B\u044B. \u041D\u0430\u0438\u0431\u043E\u043B\u0435\u0435 \u0438\u0441\u043F\u043E\u043B\u044C\u0437\u0443\u0435\u043C\u044B\u0439 \u0432\u0430\u0440\u0438\u0430\u043D\u0442 \u0444\u043E\u0440\u043C\u0443\u043B\u044B: \u0421\u043B\u0435\u0434\u0443\u044E\u0449\u0438\u0439 \u0447\u043B\u0435\u043D \u0432 \u044D\u0442\u043E ; \u0442\u0430\u043A\u0438\u043C \u043E\u0431\u0440\u0430\u0437\u043E\u043C \u0431\u043E\u043B\u0435\u0435 \u0442\u043E\u0447\u043D\u0430\u044F \u0430\u043F\u043F\u0440\u043E\u043A\u0441\u0438\u043C\u0430\u0446\u0438\u044F: \u0447\u0442\u043E \u044D\u043A\u0432\u0438\u0432\u0430\u043B\u0435\u043D\u0442\u043D\u043E \u0427\u0430\u0441\u0442\u043E \u0444\u043E\u0440\u043C\u0443\u043B\u0443 \u0421\u0442\u0438\u0440\u043B\u0438\u043D\u0433\u0430 \u0437\u0430\u043F\u0438\u0441\u044B\u0432\u0430\u044E\u0442 \u0432 \u0432\u0438\u0434\u0435 \u0433\u0434\u0435 , .\u0411\u043E\u043B\u0435\u0435 \u0442\u043E\u0447\u043D\u0443\u044E \u043E\u0446\u0435\u043D\u043A\u0443 \u0434\u0430\u0451\u0442 \u0444\u043E\u0440\u043C\u0443\u043B\u0430 \u0433\u0434\u0435 , . \u0412 \u043F\u043E\u0441\u043B\u0435\u0434\u043D\u0435\u0439 \u0444\u043E\u0440\u043C\u0443\u043B\u0435 \u043C\u0430\u043A\u0441\u0438\u043C\u0430\u043B\u044C\u043D\u043E\u0435 \u0437\u043D\u0430\u0447\u0435\u043D\u0438\u0435 \u0432 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043B\u044C\u043D\u043E\u0441\u0442\u0438 \u043C\u0435\u043D\u044C\u0448\u0435 1 \u0438 \u043F\u0440\u0438\u043C\u0435\u0440\u043D\u043E \u0440\u0430\u0432\u043D\u043E 0,7509. \u0424\u043E\u0440\u043C\u0443\u043B\u0430 \u0421\u0442\u0438\u0440\u043B\u0438\u043D\u0433\u0430 \u044F\u0432\u043B\u044F\u0435\u0442\u0441\u044F \u043F\u0440\u0438\u0431\u043B\u0438\u0436\u0435\u043D\u0438\u0435\u043C, \u043F\u043E\u043B\u0443\u0447\u0435\u043D\u043D\u044B\u043C \u0438\u0437 \u0440\u0430\u0437\u043B\u043E\u0436\u0435\u043D\u0438\u044F \u0444\u0430\u043A\u0442\u043E\u0440\u0438\u0430\u043B\u0430 \u0432 \u0440\u044F\u0434 \u0421\u0442\u0438\u0440\u043B\u0438\u043D\u0433\u0430, \u043A\u043E\u0442\u043E\u0440\u044B\u0439 \u043F\u0440\u0438 \u0438\u043C\u0435\u0435\u0442 \u0432\u0438\u0434 \u0433\u0434\u0435 \u2014 \u0447\u0438\u0441\u043B\u0430 \u0411\u0435\u0440\u043D\u0443\u043B\u043B\u0438 \u0441 \u043D\u043E\u043C\u0435\u0440\u043E\u043C . \u0412 \u044D\u0442\u043E\u0439 \u0444\u043E\u0440\u043C\u0443\u043B\u0435 \u0438\u0441\u043F\u043E\u043B\u044C\u0437\u0443\u0435\u0442\u0441\u044F \u0441\u0438\u043C\u0432\u043E\u043B \u044D\u043A\u0432\u0438\u0432\u0430\u043B\u0435\u043D\u0442\u043D\u043E\u0441\u0442\u0438 \u0432\u043C\u0435\u0441\u0442\u043E \u0440\u0430\u0432\u0435\u043D\u0441\u0442\u0432\u0430, \u0442\u0430\u043A \u043A\u0430\u043A \u0440\u044F\u0434 \u0440\u0430\u0441\u0445\u043E\u0434\u0438\u0442\u0441\u044F \u043F\u0440\u0438 \u043A\u0430\u0436\u0434\u043E\u043C \u0444\u0438\u043A\u0441\u0438\u0440\u043E\u0432\u0430\u043D\u043D\u043E\u043C , \u043E\u0434\u043D\u0430\u043A\u043E \u043E\u043D \u044F\u0432\u043B\u044F\u0435\u0442\u0441\u044F \u0430\u0441\u0438\u043C\u043F\u0442\u043E\u0442\u0438\u0447\u0435\u0441\u043A\u0438\u043C \u0440\u0430\u0437\u043B\u043E\u0436\u0435\u043D\u0438\u0435\u043C \u0444\u0430\u043A\u0442\u043E\u0440\u0438\u0430\u043B\u0430 \u043F\u0440\u0438 ."@ru .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/ontology/abstract>	"De formule van Stirling is een benadering voor de faculteit van grote getallen. De formule luidt: Dit betekent ruwweg dat het rechterlid voor voldoende grote als benadering geldt voor . Om precies te zijn: De formule is het resultaat van de eerste drie termen uit de ontwikkeling: De formule komt ook voor met alleen de eerste twee termen: , wat asymptotisch op hetzelfde neerkomt. De formule werd ontdekt door De Moivre in een iets andere vorm, namelijk: James Stirling, naar wie de formule genoemd is, toonde aan dat de constante gelijk is aan ."@nl .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/property/wikiPageUsesTemplate>	<http://dbpedia.org/resource/Template:OEIS_link> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/ontology/wikiPageID>	"151783"^^<http://www.w3.org/2001/XMLSchema#integer> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2002/07/owl#sameAs>	<https://global.dbpedia.org/id/4Mq8r> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2002/07/owl#sameAs>	<http://ru.dbpedia.org/resource/\u0424\u043E\u0440\u043C\u0443\u043B\u0430_\u0421\u0442\u0438\u0440\u043B\u0438\u043D\u0433\u0430> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2002/07/owl#sameAs>	<http://sv.dbpedia.org/resource/Stirlings_formel> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/ontology/abstract>	"In matematica l'approssimazione di Stirling o formula di Stirling o formula approssimata di Stirling \u00E8 un'approssimazione per fattoriali grandi. Deve il suo nome al matematico scozzese James Stirling (1692-1770). La formulazione corretta \u00E8: che viene scritta spesso come: Per valori elevati di n il secondo membro della formula fornisce una buona approssimazione di n! che si pu\u00F2 calcolare rapidamente e facilmente. Ad esempio la formula per 30! fornisce l'approssimazione 2,6452 \u00D7 1032, mentre un valore pi\u00F9 preciso \u00E8 2,6525 \u00D7 1032; in questo caso si ha una discrepanza minore dello 0,3%, pi\u00F9 precisamente:"@it .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2000/01/rdf-schema#comment>	"\u0424\u043E\u0440\u043C\u0443\u043B\u0430 \u0421\u0442\u0456\u0440\u043B\u0456\u043D\u0491\u0430 \u0454 \u043D\u0430\u0431\u043B\u0438\u0436\u0435\u043D\u043D\u044F\u043C \u0434\u043B\u044F \u0444\u0430\u043A\u0442\u043E\u0440\u0456\u0430\u043B\u0456\u0432 \u043F\u0440\u0438 \u0432\u0435\u043B\u0438\u043A\u0438\u0445 \u0437\u043D\u0430\u0447\u0435\u043D\u043D\u044F\u0445 n, \u043D\u0430\u0437\u0432\u0430\u043D\u0430 \u043D\u0430 \u0447\u0435\u0441\u0442\u044C \u0414\u0436\u0435\u0439\u043C\u0441\u0430 \u0421\u0442\u0456\u0440\u043B\u0456\u043D\u0491\u0430. \u0424\u043E\u0440\u043C\u0430\u043B\u044C\u043D\u0435 \u0442\u0432\u0435\u0440\u0434\u0436\u0435\u043D\u043D\u044F \u0444\u043E\u0440\u043C\u0443\u043B\u0438 \u0430\u0431\u043E"@uk .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/property/wikiPageUsesTemplate>	<http://dbpedia.org/resource/Template:Commons_category> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2002/07/owl#sameAs>	<http://uk.dbpedia.org/resource/\u0424\u043E\u0440\u043C\u0443\u043B\u0430_\u0421\u0442\u0456\u0440\u043B\u0456\u043D\u0491\u0430> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Stirling_numbers_of_the_first_kind> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Taylor_series> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2000/01/rdf-schema#comment>	"En matem\u00E0tiques, l'aproximaci\u00F3 de Stirling (o f\u00F3rmula de Stirling) \u00E9s una aproximaci\u00F3 pels factorials, que dona un equivalent del factorial d'un enter natural n quan n tendeix a l'infinit: que tamb\u00E9 s'escriu sovint aix\u00ED: on e representa el nombre e. \u00C9s una aproximaci\u00F3 de bona qualitat, donant lloc a resultats precisos fins i tot per a valors petits de n. Porta el nom de James Stirling, tot i que es va afirmar per primera vegada per Abraham de Moivre. La f\u00F3rmula que es fa servir normalment en aplicacions \u00E9s , o per a tots els nombres enters positius n. Aix\u00ED, la relaci\u00F3 de \u00E9s sempre entre i ."@ca .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/1999/02/22-rdf-syntax-ns#type>	<http://dbpedia.org/class/yago/Communication100033020> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/ontology/abstract>	"\u0641\u064A \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0627\u062A\u060C \u062A\u0642\u0631\u064A\u0628 \u0633\u062A\u064A\u0631\u0644\u064A\u0646\u063A (\u0628\u0627\u0644\u0625\u0646\u062C\u0644\u064A\u0632\u064A\u0629: Stirling's approximation)\u200F (\u0623\u0648 \u0635\u064A\u063A\u0629 \u0633\u062A\u064A\u0631\u0644\u064A\u0646\u063A (\u0628\u0627\u0644\u0625\u0646\u062C\u0644\u064A\u0632\u064A\u0629: Stirling's formula)\u200F) \u0647\u0648 \u0635\u064A\u063A\u0629 \u0631\u064A\u0627\u0636\u064A\u0629 \u062A\u0633\u062A\u062E\u062F\u0645 \u0644\u062A\u0642\u0631\u064A\u0628 \u0642\u064A\u0645 \u0627\u0644\u0639\u0627\u0645\u0644\u064A \u0627\u0644\u0643\u0628\u064A\u0631\u0629. \u0633\u0645\u064A \u0643\u0630\u0644\u0643 \u0646\u0633\u0628\u0629 \u0625\u0644\u0649 \u0639\u0627\u0644\u0645 \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0627\u062A \u062C\u064A\u0645\u0633 \u0633\u062A\u064A\u0631\u0644\u064A\u0646\u063A."@ar .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2000/01/rdf-schema#label>	"\u0424\u043E\u0440\u043C\u0443\u043B\u0430 \u0421\u0442\u0438\u0440\u043B\u0438\u043D\u0433\u0430"@ru .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2002/07/owl#sameAs>	<http://ar.dbpedia.org/resource/\u062A\u0642\u0631\u064A\u0628_\u0633\u062A\u064A\u0631\u0644\u064A\u0646\u063A> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2002/07/owl#sameAs>	<http://be.dbpedia.org/resource/\u0424\u043E\u0440\u043C\u0443\u043B\u0430_\u0421\u0442\u044B\u0440\u043B\u0456\u043D\u0433\u0430> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2002/07/owl#sameAs>	<http://yago-knowledge.org/resource/Stirling\u0027s_approximation> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/1999/02/22-rdf-syntax-ns#type>	<http://dbpedia.org/class/yago/ProblemSolving105796750> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Mathematics> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/File:Mplwp_factorial_gamma_stirling.svg> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Big-O_notation> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2002/07/owl#sameAs>	<http://es.dbpedia.org/resource/F\u00F3rmula_de_Stirling> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2000/01/rdf-schema#label>	"Stirlings formel"@sv .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/1999/02/22-rdf-syntax-ns#type>	<http://dbpedia.org/class/yago/PsychologicalFeature100023100> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/property/wikiPageUsesTemplate>	<http://dbpedia.org/resource/Template:R> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/1999/02/22-rdf-syntax-ns#type>	<http://dbpedia.org/class/yago/Abstraction100002137> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/1999/02/22-rdf-syntax-ns#type>	<http://dbpedia.org/class/yago/Process105701363> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2000/01/rdf-schema#label>	"Stirling\u016Fv vzorec"@cs .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/ontology/wikiPageLength>	"23714"^^<http://www.w3.org/2001/XMLSchema#nonNegativeInteger> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/1999/02/22-rdf-syntax-ns#type>	<http://dbpedia.org/class/yago/Statement106722453> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Riemann\u2013Siegel_theta_function> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2002/07/owl#sameAs>	<http://rdf.freebase.com/ns/m.013rp2> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2002/07/owl#sameAs>	<http://tr.dbpedia.org/resource/Stirling_yakla\u015F\u0131m\u0131> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2000/01/rdf-schema#comment>	"Wz\u00F3r Stirlinga \u2013 wz\u00F3r pozwalaj\u0105cy obliczy\u0107 w przybli\u017Ceniu warto\u015B\u0107 silni: Wz\u00F3r ten daje dobre przybli\u017Cenie dla du\u017Cych liczb Formalnie: Przybli\u017Cona, cz\u0119sto u\u017Cywana posta\u0107 logarytmiczna: Nazwa pochodzi od nazwiska szkockiego matematyka: Jamesa Stirlinga."@pl .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/property/wikiPageUsesTemplate>	<http://dbpedia.org/resource/Template:Reflist> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/1999/02/22-rdf-syntax-ns#type>	<http://dbpedia.org/class/yago/Message106598915> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2000/01/rdf-schema#comment>	"Stirling\u016Fv vzorec (t\u00E9\u017E Stirlingova formule) je nejzn\u00E1m\u011Bj\u0161\u00ED aproximac\u00ED faktori\u00E1lu pro vysok\u00E9 hodnoty argumentu. Stejn\u011B dob\u0159e jde vzorec pou\u017E\u00EDt i pro aproximaci gama funkce, kter\u00E1 v podstat\u011B p\u0159edstavuje zobecn\u011Bn\u00ED faktori\u00E1lu a to na obor komplexn\u00EDch \u010D\u00EDsel. Je pojmenov\u00E1n po skotsk\u00E9m matematikovi . Stirling\u016Fv vzorec zn\u00ED: Symbolu p\u0159ibli\u017En\u011B je nutno rozum\u011Bt tak, \u017Ee plat\u00ED: S rostouc\u00EDm tedy Stirling\u016Fv vzorec procentu\u00E1ln\u011B \u010D\u00EDm d\u00E1l l\u00E9pe aproximuje faktori\u00E1l. Absolutn\u00ED odchylka faktori\u00E1lu a jeho Stirlingovy aproximace ov\u0161em k nule jde."@cs .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://purl.org/dc/terms/subject>	<http://dbpedia.org/resource/Category:Approximations> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2002/07/owl#sameAs>	<http://no.dbpedia.org/resource/Stirlings_formel> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/property/title>	"Stirling's approximation"@en .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/ontology/abstract>	"\u039F \u03C4\u03CD\u03C0\u03BF\u03C2 \u03C4\u03BF\u03C5 \u03A3\u03C4\u03AF\u03C1\u03BB\u03B9\u03BD\u03B3\u03BA (\u03AE \u03A3\u03C4\u03AD\u03C1\u03BB\u03B9\u03BD\u03B3\u03BA) \u03B4\u03AF\u03BD\u03B5\u03B9 \u03BC\u03AF\u03B1 \u03C0\u03C1\u03BF\u03C3\u03AD\u03B3\u03B3\u03B9\u03C3\u03B7 \u03C4\u03C9\u03BD \u03C0\u03B1\u03C1\u03B1\u03B3\u03BF\u03BD\u03C4\u03B9\u03BA\u03CE\u03BD \u03BC\u03B5\u03B3\u03AC\u03BB\u03C9\u03BD \u03B1\u03C1\u03B9\u03B8\u03BC\u03CE\u03BD \u03BA\u03B1\u03B9 \u03BF\u03BD\u03BF\u03BC\u03AC\u03C3\u03C4\u03B7\u03BA\u03B5 \u03AD\u03C4\u03C3\u03B9 \u03C0\u03C1\u03BF\u03C2 \u03C4\u03B9\u03BC\u03AE\u03BD \u03C4\u03BF\u03C5 \u03BC\u03B1\u03B8\u03B7\u03BC\u03B1\u03C4\u03B9\u03BA\u03BF\u03CD . \u039F \u03B1\u03BA\u03C1\u03B9\u03B2\u03AE\u03C2 \u03C4\u03CD\u03C0\u03BF\u03C2 \u03B5\u03AF\u03BD\u03B1\u03B9: \u0393\u03B9\u03B1 \u03B4\u03B5 \u03C4\u03BF \u03C6\u03C5\u03C3\u03B9\u03BA\u03CC \u03BB\u03BF\u03B3\u03AC\u03C1\u03B9\u03B8\u03BC\u03BF \u03C4\u03BF\u03C5 \u03C0\u03B1\u03C1\u03B1\u03B3\u03BF\u03BD\u03C4\u03B9\u03BA\u03BF\u03CD \u03BC\u03B5\u03B3\u03AC\u03BB\u03C9\u03BD \u03B1\u03C1\u03B9\u03B8\u03BC\u03CE\u03BD \u03B5\u03AF\u03BD\u03B1\u03B9 \u03BA\u03B1\u03BB\u03AE \u03BA\u03B1\u03B9 \u03B7 \u03C0\u03C1\u03BF\u03C3\u03AD\u03B3\u03B3\u03B9\u03C3\u03B7 \u03C0\u03B1\u03C1\u03B1\u03BB\u03B5\u03AF\u03C0\u03BF\u03BD\u03C4\u03B1\u03C2 \u03C4\u03BF\u03BD \u03CC\u03C1\u03BF: \u03BF\u03C0\u03CC\u03C4\u03B5 \u03C4\u03B5\u03BB\u03B9\u03BA\u03AC:"@el .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/property/mode>	"cs2"@en .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/1999/02/22-rdf-syntax-ns#type>	<http://dbpedia.org/class/yago/HigherCognitiveProcess105770664> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Category:Approximations> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/1999/02/22-rdf-syntax-ns#type>	<http://dbpedia.org/class/yago/MathematicalRelation113783581> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2000/01/rdf-schema#comment>	"\uC218\uD559\uC5D0\uC11C \uC2A4\uD138\uB9C1 \uADFC\uC0AC(\uC601\uC5B4: Stirling\u2019s approximation) \uB610\uB294 \uC2A4\uD138\uB9C1 \uACF5\uC2DD(\uC601\uC5B4: Stirling\u2019s formula)\uC740 \uD070 \uACC4\uC2B9\uC744 \uAD6C\uD558\uB294 \uADFC\uC0AC\uBC95\uC774\uB2E4."@ko .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2002/07/owl#sameAs>	<http://lt.dbpedia.org/resource/Stirlingo_formul\u0117> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/1999/02/22-rdf-syntax-ns#type>	<http://dbpedia.org/class/yago/WikicatTheoremsInAnalysis> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2000/01/rdf-schema#comment>	"\u0412 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0435 \u0444\u043E\u0440\u043C\u0443\u043B\u0430 \u0421\u0442\u0438\u0440\u043B\u0438\u043D\u0433\u0430 (\u0442\u0430\u043A\u0436\u0435 \u0444\u043E\u0440\u043C\u0443\u043B\u0430 \u041C\u0443\u0430\u0432\u0440\u0430 \u2014 \u0421\u0442\u0438\u0440\u043B\u0438\u043D\u0433\u0430) \u2014 \u0444\u043E\u0440\u043C\u0443\u043B\u0430 \u0434\u043B\u044F \u043F\u0440\u0438\u0431\u043B\u0438\u0436\u0451\u043D\u043D\u043E\u0433\u043E \u0432\u044B\u0447\u0438\u0441\u043B\u0435\u043D\u0438\u044F \u0444\u0430\u043A\u0442\u043E\u0440\u0438\u0430\u043B\u0430 \u0438 \u0433\u0430\u043C\u043C\u0430-\u0444\u0443\u043D\u043A\u0446\u0438\u0438. \u041D\u0430\u0437\u0432\u0430\u043D\u0430 \u0432 \u0447\u0435\u0441\u0442\u044C \u0414\u0436\u0435\u0439\u043C\u0441\u0430 \u0421\u0442\u0438\u0440\u043B\u0438\u043D\u0433\u0430 \u0438 \u0410\u0431\u0440\u0430\u0445\u0430\u043C\u0430 \u0434\u0435 \u041C\u0443\u0430\u0432\u0440\u0430, \u043F\u043E\u0441\u043B\u0435\u0434\u043D\u0438\u0439 \u0441\u0447\u0438\u0442\u0430\u0435\u0442\u0441\u044F \u0430\u0432\u0442\u043E\u0440\u043E\u043C \u0444\u043E\u0440\u043C\u0443\u043B\u044B. \u041D\u0430\u0438\u0431\u043E\u043B\u0435\u0435 \u0438\u0441\u043F\u043E\u043B\u044C\u0437\u0443\u0435\u043C\u044B\u0439 \u0432\u0430\u0440\u0438\u0430\u043D\u0442 \u0444\u043E\u0440\u043C\u0443\u043B\u044B: \u0421\u043B\u0435\u0434\u0443\u044E\u0449\u0438\u0439 \u0447\u043B\u0435\u043D \u0432 \u044D\u0442\u043E ; \u0442\u0430\u043A\u0438\u043C \u043E\u0431\u0440\u0430\u0437\u043E\u043C \u0431\u043E\u043B\u0435\u0435 \u0442\u043E\u0447\u043D\u0430\u044F \u0430\u043F\u043F\u0440\u043E\u043A\u0441\u0438\u043C\u0430\u0446\u0438\u044F: \u0447\u0442\u043E \u044D\u043A\u0432\u0438\u0432\u0430\u043B\u0435\u043D\u0442\u043D\u043E \u0427\u0430\u0441\u0442\u043E \u0444\u043E\u0440\u043C\u0443\u043B\u0443 \u0421\u0442\u0438\u0440\u043B\u0438\u043D\u0433\u0430 \u0437\u0430\u043F\u0438\u0441\u044B\u0432\u0430\u044E\u0442 \u0432 \u0432\u0438\u0434\u0435 \u0433\u0434\u0435 , .\u0411\u043E\u043B\u0435\u0435 \u0442\u043E\u0447\u043D\u0443\u044E \u043E\u0446\u0435\u043D\u043A\u0443 \u0434\u0430\u0451\u0442 \u0444\u043E\u0440\u043C\u0443\u043B\u0430 \u0433\u0434\u0435 , . \u0412 \u043F\u043E\u0441\u043B\u0435\u0434\u043D\u0435\u0439 \u0444\u043E\u0440\u043C\u0443\u043B\u0435 \u043C\u0430\u043A\u0441\u0438\u043C\u0430\u043B\u044C\u043D\u043E\u0435 \u0437\u043D\u0430\u0447\u0435\u043D\u0438\u0435 \u0432 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043B\u044C\u043D\u043E\u0441\u0442\u0438 \u043C\u0435\u043D\u044C\u0448\u0435 1 \u0438 \u043F\u0440\u0438\u043C\u0435\u0440\u043D\u043E \u0440\u0430\u0432\u043D\u043E 0,7509. \u0433\u0434\u0435 \u2014 \u0447\u0438\u0441\u043B\u0430 \u0411\u0435\u0440\u043D\u0443\u043B\u043B\u0438 \u0441 \u043D\u043E\u043C\u0435\u0440\u043E\u043C ."@ru .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/ontology/abstract>	"Stirlings formel \u00E4r en approximation f\u00F6r stora fakulteter, uppt\u00E4ckt av Abraham de Moivre, men namngiven efter James Stirling. Anv\u00E4nds exempelvis inom statistisk mekanik d\u00E4r n \u00E4r av ordningen \u221D1023, men \u00E4ven f\u00F6r n \u2265 5 ger den acceptabel noggrannhet. Formeln kan skrivas vilket ofta uttrycks som (Se limes, kvadratrot, \u03C0, e.) F\u00F6r stora n s\u00E5 \u00E4r h\u00F6gerledet en god approximation f\u00F6r n! och g\u00E5r mycket snabbare och enklare att ber\u00E4kna. F\u00F6r exempelvis 30! ger approximationen v\u00E4rdet 2,6451 \u00B7 1032 medan det verkliga v\u00E4rdet \u00E4r 2,6525 \u00B7 1032. Formeln kan \u00E4ven uttryckas som eller om n >> ln n,"@sv .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2002/07/owl#sameAs>	<http://scn.dbpedia.org/resource/Formula_di_Stirling> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2000/01/rdf-schema#label>	"Stirling's approximation"@en .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2000/01/rdf-schema#label>	"Formule de Stirling"@fr .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/property/wikiPageUsesTemplate>	<http://dbpedia.org/resource/Template:Clarify> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/ontology/wikiPageExternalLink>	<https://projecteuclid.org/euclid.rae/1184700051> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/ontology/abstract>	"\u0424\u043E\u0440\u043C\u0443\u043B\u0430 \u0421\u0442\u0456\u0440\u043B\u0456\u043D\u0491\u0430 \u0454 \u043D\u0430\u0431\u043B\u0438\u0436\u0435\u043D\u043D\u044F\u043C \u0434\u043B\u044F \u0444\u0430\u043A\u0442\u043E\u0440\u0456\u0430\u043B\u0456\u0432 \u043F\u0440\u0438 \u0432\u0435\u043B\u0438\u043A\u0438\u0445 \u0437\u043D\u0430\u0447\u0435\u043D\u043D\u044F\u0445 n, \u043D\u0430\u0437\u0432\u0430\u043D\u0430 \u043D\u0430 \u0447\u0435\u0441\u0442\u044C \u0414\u0436\u0435\u0439\u043C\u0441\u0430 \u0421\u0442\u0456\u0440\u043B\u0456\u043D\u0491\u0430. \u0424\u043E\u0440\u043C\u0430\u043B\u044C\u043D\u0435 \u0442\u0432\u0435\u0440\u0434\u0436\u0435\u043D\u043D\u044F \u0444\u043E\u0440\u043C\u0443\u043B\u0438 \u0430\u0431\u043E"@uk .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2000/01/rdf-schema#label>	"Wz\u00F3r Stirlinga"@pl .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/ns/prov#wasDerivedFrom>	<http://en.wikipedia.org/wiki/Stirling\u0027s_approximation?oldid=1124298777&ns=0> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://xmlns.com/foaf/0.1/isPrimaryTopicOf>	<http://en.wikipedia.org/wiki/Stirling\u0027s_approximation> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/1999/02/22-rdf-syntax-ns#type>	<http://dbpedia.org/class/yago/Proposition106750804> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2000/01/rdf-schema#label>	"Stirlingen hurbilketa"@eu .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Method_of_steepest_descent> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/ontology/abstract>	"En matem\u00E1ticas, la f\u00F3rmula de Stirling es una aproximaci\u00F3n para factoriales grandes. Lleva el nombre en honor al matem\u00E1tico escoc\u00E9s del siglo XVIII James Stirling. La aproximaci\u00F3n se expresa como para n suficientemente grande, donde ln es el logaritmo natural."@es .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2002/07/owl#sameAs>	<http://ur.dbpedia.org/resource/\u0633\u0679\u0631\u0644\u0646\u06AF_\u06A9\u0644\u06CC\u06C1> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/ontology/wikiPageExternalLink>	<https://archive.org/details/asymptoticsmelli0000pari> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/ontology/abstract>	"In mathematics, Stirling's approximation (or Stirling's formula) is an approximation for factorials. It is a good approximation, leading to accurate results even for small values of . It is named after James Stirling, though a related but less precise result was first stated by Abraham de Moivre. One way of stating the approximation involves the logarithm of the factorial: where the big O notation means that, for all sufficiently large values of , the difference between and will be at most proportional to the logarithm. In computer science applications such as the worst-case lower bound for comparison sorting, it is convenient to use instead the binary logarithm, giving the equivalent form The error term in either base can be expressed more precisely as , corresponding to an approximate formula for the factorial itself,Here the sign means that the two quantities are asymptotic, that is, that their ratio tends to 1 as tends to infinity. The following version of the bound holds for all , rather than only asymptotically:"@en .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2000/01/rdf-schema#label>	"Stirlingformel"@de .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2002/07/owl#sameAs>	<http://ckb.dbpedia.org/resource/\u0646\u0632\u06CC\u06A9\u062E\u0633\u062A\u0646\u06D5\u0648\u06D5\u06CC_\u0626\u06CE\u0633\u062A\u0631\u0644\u06CC\u0646\u06AF> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2000/01/rdf-schema#label>	"\uC2A4\uD138\uB9C1 \uADFC\uC0AC"@ko .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://purl.org/dc/terms/subject>	<http://dbpedia.org/resource/Category:Gamma_and_related_functions> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2002/07/owl#sameAs>	<http://fr.dbpedia.org/resource/Formule_de_Stirling> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2002/07/owl#sameAs>	<http://de.dbpedia.org/resource/Stirlingformel> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Category:Theorems_in_analysis> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2000/01/rdf-schema#comment>	"In mathematics, Stirling's approximation (or Stirling's formula) is an approximation for factorials. It is a good approximation, leading to accurate results even for small values of . It is named after James Stirling, though a related but less precise result was first stated by Abraham de Moivre. One way of stating the approximation involves the logarithm of the factorial:"@en .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/1999/02/22-rdf-syntax-ns#type>	<http://dbpedia.org/class/yago/Cognition100023271> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Category:Gamma_and_related_functions> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2002/07/owl#sameAs>	<http://sk.dbpedia.org/resource/Stirlingova_aproxim\u00E1cia> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Comparison_sort> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/ontology/abstract>	"Stirling\u016Fv vzorec (t\u00E9\u017E Stirlingova formule) je nejzn\u00E1m\u011Bj\u0161\u00ED aproximac\u00ED faktori\u00E1lu pro vysok\u00E9 hodnoty argumentu. Stejn\u011B dob\u0159e jde vzorec pou\u017E\u00EDt i pro aproximaci gama funkce, kter\u00E1 v podstat\u011B p\u0159edstavuje zobecn\u011Bn\u00ED faktori\u00E1lu a to na obor komplexn\u00EDch \u010D\u00EDsel. Je pojmenov\u00E1n po skotsk\u00E9m matematikovi . Stirling\u016Fv vzorec zn\u00ED: Symbolu p\u0159ibli\u017En\u011B je nutno rozum\u011Bt tak, \u017Ee plat\u00ED: S rostouc\u00EDm tedy Stirling\u016Fv vzorec procentu\u00E1ln\u011B \u010D\u00EDm d\u00E1l l\u00E9pe aproximuje faktori\u00E1l. Absolutn\u00ED odchylka faktori\u00E1lu a jeho Stirlingovy aproximace ov\u0161em k nule jde. P\u0159edstavu o p\u0159esnosti tohoto vztahu si lze ud\u011Blat z procentu\u00E1ln\u00ED odchylky faktori\u00E1lu od Stirlingova vzorce. Tato odchylka je v\u017Edy kladn\u00E1, tedy Stirling\u016Fv vzorec je v\u017Edy o n\u011Bco men\u0161\u00ED ne\u017E dan\u00FD faktori\u00E1l. Z tabulky je patrn\u00E9, \u017Ee ji\u017E pro je odchylka docela mal\u00E1. Pro nem\u00E1 Stirling\u016Fv vzorec smysl (nen\u00ED-li speci\u00E1ln\u011B definov\u00E1na nula na nultou). Stirling\u016Fv vzorec se pou\u017E\u00EDv\u00E1 hlavn\u011B p\u0159i v\u00FDpo\u010Dtu limit, kde vystupuje faktori\u00E1l. Ve fyzice nal\u00E9z\u00E1 velk\u00E9 uplatn\u011Bn\u00ED ve statistick\u00E9 fyzice."@cs .
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<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/ontology/abstract>	"Matematikaren alorrean, Stirlingen hurbilketa edo Stirlingen formula deritzona, faktorialak hurbiltzeko erabiltzen den formula bat da. Beste era batera esanda, zenbaki altuen faktoriala kalkulatzea ez da batere erraza eta formula honek balio altu horretatik oso hurbil dagoen zenbaki bat itzultzen du. Hurbilketa hau oso zehatza eta erabilgarria da balio handiko zenbakien faktoriala lortzeko edota adierazpen bat beste adierazpen hurbil batera murrizteko. James Stirling, XVIII. mendeko matematikari eskoziarrari esker, n infinitura doanean ondoko limitea dugu: Beraz, esan dezakegu n zenbaki altu baten faktorialaren hurbilketa ondokoa dela: Era berean, faktorialen logaritmoak kalkulatzeko ere honela erabili daiteke:"@eu .
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<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/ontology/abstract>	"En matem\u00E0tiques, l'aproximaci\u00F3 de Stirling (o f\u00F3rmula de Stirling) \u00E9s una aproximaci\u00F3 pels factorials, que dona un equivalent del factorial d'un enter natural n quan n tendeix a l'infinit: que tamb\u00E9 s'escriu sovint aix\u00ED: on e representa el nombre e. \u00C9s una aproximaci\u00F3 de bona qualitat, donant lloc a resultats precisos fins i tot per a valors petits de n. Porta el nom de James Stirling, tot i que es va afirmar per primera vegada per Abraham de Moivre. La f\u00F3rmula que es fa servir normalment en aplicacions \u00E9s , o o, per exemple, en el pitjor dels casos del l\u00EDmit inferior per (pel canvi de la base del logaritme), (en notaci\u00F3 O Gran). El seg\u00FCent terme en O(ln n) \u00E9s 12ln(2\u03C0n); per tant, una variant m\u00E9s precisa de la f\u00F3rmula \u00E9s on el signe ~ vol dir que les dues quantitats s\u00F3n asimpt\u00F2tiques, \u00E9s a dir, la seva relaci\u00F3 tendeix a 1 quan n tendeix a infinit. Tamb\u00E9 \u00E9s possible donar una versi\u00F3 de la f\u00F3rmula de Stirling amb els l\u00EDmits v\u00E0lids per a tots els enters positius n, en lloc de l'asimpt\u00F2tica, que \u00E9s per a tots els nombres enters positius n. Aix\u00ED, la relaci\u00F3 de \u00E9s sempre entre i ."@ca .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2000/01/rdf-schema#comment>	"\u039F \u03C4\u03CD\u03C0\u03BF\u03C2 \u03C4\u03BF\u03C5 \u03A3\u03C4\u03AF\u03C1\u03BB\u03B9\u03BD\u03B3\u03BA (\u03AE \u03A3\u03C4\u03AD\u03C1\u03BB\u03B9\u03BD\u03B3\u03BA) \u03B4\u03AF\u03BD\u03B5\u03B9 \u03BC\u03AF\u03B1 \u03C0\u03C1\u03BF\u03C3\u03AD\u03B3\u03B3\u03B9\u03C3\u03B7 \u03C4\u03C9\u03BD \u03C0\u03B1\u03C1\u03B1\u03B3\u03BF\u03BD\u03C4\u03B9\u03BA\u03CE\u03BD \u03BC\u03B5\u03B3\u03AC\u03BB\u03C9\u03BD \u03B1\u03C1\u03B9\u03B8\u03BC\u03CE\u03BD \u03BA\u03B1\u03B9 \u03BF\u03BD\u03BF\u03BC\u03AC\u03C3\u03C4\u03B7\u03BA\u03B5 \u03AD\u03C4\u03C3\u03B9 \u03C0\u03C1\u03BF\u03C2 \u03C4\u03B9\u03BC\u03AE\u03BD \u03C4\u03BF\u03C5 \u03BC\u03B1\u03B8\u03B7\u03BC\u03B1\u03C4\u03B9\u03BA\u03BF\u03CD . \u039F \u03B1\u03BA\u03C1\u03B9\u03B2\u03AE\u03C2 \u03C4\u03CD\u03C0\u03BF\u03C2 \u03B5\u03AF\u03BD\u03B1\u03B9: \u0393\u03B9\u03B1 \u03B4\u03B5 \u03C4\u03BF \u03C6\u03C5\u03C3\u03B9\u03BA\u03CC \u03BB\u03BF\u03B3\u03AC\u03C1\u03B9\u03B8\u03BC\u03BF \u03C4\u03BF\u03C5 \u03C0\u03B1\u03C1\u03B1\u03B3\u03BF\u03BD\u03C4\u03B9\u03BA\u03BF\u03CD \u03BC\u03B5\u03B3\u03AC\u03BB\u03C9\u03BD \u03B1\u03C1\u03B9\u03B8\u03BC\u03CE\u03BD \u03B5\u03AF\u03BD\u03B1\u03B9 \u03BA\u03B1\u03BB\u03AE \u03BA\u03B1\u03B9 \u03B7 \u03C0\u03C1\u03BF\u03C3\u03AD\u03B3\u03B3\u03B9\u03C3\u03B7 \u03C0\u03B1\u03C1\u03B1\u03BB\u03B5\u03AF\u03C0\u03BF\u03BD\u03C4\u03B1\u03C2 \u03C4\u03BF\u03BD \u03CC\u03C1\u03BF: \u03BF\u03C0\u03CC\u03C4\u03B5 \u03C4\u03B5\u03BB\u03B9\u03BA\u03AC:"@el .
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<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2000/01/rdf-schema#comment>	"In matematica l'approssimazione di Stirling o formula di Stirling o formula approssimata di Stirling \u00E8 un'approssimazione per fattoriali grandi. Deve il suo nome al matematico scozzese James Stirling (1692-1770). La formulazione corretta \u00E8: che viene scritta spesso come:"@it .
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<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/ontology/abstract>	"La formule de Stirling, du nom du math\u00E9maticien \u00E9cossais James Stirling, donne un \u00E9quivalent de la factorielle d'un entier naturel n quand n tend vers l'infini : que l'on trouve souvent \u00E9crite ainsi : o\u00F9 le nombre e d\u00E9signe la base de l'exponentielle."@fr .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2000/01/rdf-schema#comment>	"Stirlings formel \u00E4r en approximation f\u00F6r stora fakulteter, uppt\u00E4ckt av Abraham de Moivre, men namngiven efter James Stirling. Anv\u00E4nds exempelvis inom statistisk mekanik d\u00E4r n \u00E4r av ordningen \u221D1023, men \u00E4ven f\u00F6r n \u2265 5 ger den acceptabel noggrannhet. Formeln kan skrivas vilket ofta uttrycks som (Se limes, kvadratrot, \u03C0, e.) F\u00F6r stora n s\u00E5 \u00E4r h\u00F6gerledet en god approximation f\u00F6r n! och g\u00E5r mycket snabbare och enklare att ber\u00E4kna. F\u00F6r exempelvis 30! ger approximationen v\u00E4rdet 2,6451 \u00B7 1032 medan det verkliga v\u00E4rdet \u00E4r 2,6525 \u00B7 1032. Formeln kan \u00E4ven uttryckas som eller om n >> ln n,"@sv .
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<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/ontology/abstract>	"Wz\u00F3r Stirlinga \u2013 wz\u00F3r pozwalaj\u0105cy obliczy\u0107 w przybli\u017Ceniu warto\u015B\u0107 silni: Wz\u00F3r ten daje dobre przybli\u017Cenie dla du\u017Cych liczb Formalnie: Przybli\u017Cona, cz\u0119sto u\u017Cywana posta\u0107 logarytmiczna: Nazwa pochodzi od nazwiska szkockiego matematyka: Jamesa Stirlinga."@pl .
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<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2000/01/rdf-schema#comment>	"De formule van Stirling is een benadering voor de faculteit van grote getallen. De formule luidt: Dit betekent ruwweg dat het rechterlid voor voldoende grote als benadering geldt voor . Om precies te zijn: De formule is het resultaat van de eerste drie termen uit de ontwikkeling: De formule komt ook voor met alleen de eerste twee termen: , wat asymptotisch op hetzelfde neerkomt. De formule werd ontdekt door De Moivre in een iets andere vorm, namelijk: James Stirling, naar wie de formule genoemd is, toonde aan dat de constante gelijk is aan ."@nl .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2000/01/rdf-schema#comment>	"Die Stirling-Formel ist eine mathematische Formel, mit der man f\u00FCr gro\u00DFe Fakult\u00E4ten N\u00E4herungswerte berechnen kann. Sie ist nach dem schottischen Mathematiker James Stirling benannt."@de .
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<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/2000/01/rdf-schema#comment>	"En matem\u00E1ticas, la f\u00F3rmula de Stirling es una aproximaci\u00F3n para factoriales grandes. Lleva el nombre en honor al matem\u00E1tico escoc\u00E9s del siglo XVIII James Stirling. La aproximaci\u00F3n se expresa como para n suficientemente grande, donde ln es el logaritmo natural."@es .
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<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/ontology/abstract>	"Die Stirling-Formel ist eine mathematische Formel, mit der man f\u00FCr gro\u00DFe Fakult\u00E4ten N\u00E4herungswerte berechnen kann. Sie ist nach dem schottischen Mathematiker James Stirling benannt."@de .
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<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Spouge\u0027s_approximation> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Big_O_notation> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Wallis_product> .
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<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/ontology/abstract>	"Em matem\u00E1tica, a f\u00F3rmula de Stirling ou aproxima\u00E7\u00E3o de Stirling \u00E9 uma f\u00F3rmula que estabelece uma aproxima\u00E7\u00E3o assint\u00F3tica ao fatorial de um n\u00FAmero. Recebe o nome do matem\u00E1tico James Stirling. Na sua forma mais conhecida, a f\u00F3rmula escreve-se: , onde \u00E9 o n\u00FAmero de Euler, tal que O que \u00E9 uma nota\u00E7\u00E3o para o limite: . A f\u00F3rmula de Stirling \u00E9 apresentada tamb\u00E9m de outra forma, comummente utilizada em aplica\u00E7\u00F5es na f\u00EDsica, por exemplo. Quando , o logaritmo natural de um fatorial \u00E9 dado por:"@pt .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/property/wikiPageUsesTemplate>	<http://dbpedia.org/resource/Template:MathWorld> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://www.w3.org/1999/02/22-rdf-syntax-ns#type>	<http://dbpedia.org/class/yago/Estimate105803379> .
<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Hyperbolic_sine> .
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<http://dbpedia.org/resource/Stirling\u0027s_approximation>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/James_Stirling_(mathematician)> .