. . . . . . "Abelsche partielle Summation"@de . . "\u0414\u0438\u0441\u043A\u0440\u0435\u0442\u043D\u044B\u043C \u043F\u0440\u0435\u043E\u0431\u0440\u0430\u0437\u043E\u0432\u0430\u043D\u0438\u0435\u043C \u0410\u0301\u0431\u0435\u043B\u044F \u043D\u0430\u0437\u044B\u0432\u0430\u044E\u0442 \u0441\u043B\u0435\u0434\u0443\u044E\u0449\u0435\u0435 \u0442\u043E\u0436\u0434\u0435\u0441\u0442\u0432\u043E: \u0433\u0434\u0435 , \u2014 \u043F\u043E\u0441\u043B\u0435\u0434\u043E\u0432\u0430\u0442\u0435\u043B\u044C\u043D\u043E\u0441\u0442\u0438 , \u043F\u0440\u0438 \u044D\u0442\u043E\u043C \u0438 . \u042D\u0442\u043E \u043F\u0440\u0435\u043E\u0431\u0440\u0430\u0437\u043E\u0432\u0430\u043D\u0438\u0435 \u0431\u044B\u043B\u043E \u043D\u0430\u0437\u0432\u0430\u043D\u043E \u0432 \u0447\u0435\u0441\u0442\u044C \u043D\u043E\u0440\u0432\u0435\u0436\u0441\u043A\u043E\u0433\u043E \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0430 \u041D\u0438\u043B\u044C\u0441\u0430 \u0425\u0435\u043D\u0440\u0438\u043A\u0430 \u0410\u0431\u0435\u043B\u044F. \u0412 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0447\u0435\u0441\u043A\u043E\u043C \u0430\u043D\u0430\u043B\u0438\u0437\u0435 \u043E\u043D\u043E \u0438\u0441\u043F\u043E\u043B\u044C\u0437\u0443\u0435\u0442\u0441\u044F \u043F\u0440\u0438 \u0434\u043E\u043A\u0430\u0437\u0430\u0442\u0435\u043B\u044C\u0441\u0442\u0432\u0435 \u043F\u0440\u0438\u0437\u043D\u0430\u043A\u0430 \u0441\u0445\u043E\u0434\u0438\u043C\u043E\u0441\u0442\u0438 \u0414\u0438\u0440\u0438\u0445\u043B\u0435. \u041F\u0440\u0435\u043E\u0431\u0440\u0430\u0437\u043E\u0432\u0430\u043D\u0438\u0435 \u0410\u0431\u0435\u043B\u044F \u044F\u0432\u043B\u044F\u0435\u0442\u0441\u044F \u0434\u0438\u0441\u043A\u0440\u0435\u0442\u043D\u044B\u043C \u0430\u043D\u0430\u043B\u043E\u0433\u043E\u043C \u0438\u043D\u0442\u0435\u0433\u0440\u0438\u0440\u043E\u0432\u0430\u043D\u0438\u044F \u043F\u043E \u0447\u0430\u0441\u0442\u044F\u043C \u0438 \u0438\u043D\u043E\u0433\u0434\u0430 \u043D\u0430\u0437\u044B\u0432\u0430\u0435\u0442\u0441\u044F \u0441\u0443\u043C\u043C\u0438\u0440\u043E\u0432\u0430\u043D\u0438\u0435\u043C \u043F\u043E \u0447\u0430\u0441\u0442\u044F\u043C."@ru . "\u0414\u0438\u0441\u043A\u0440\u0435\u0442\u043D\u044B\u043C \u043F\u0440\u0435\u043E\u0431\u0440\u0430\u0437\u043E\u0432\u0430\u043D\u0438\u0435\u043C \u0410\u0301\u0431\u0435\u043B\u044F \u043D\u0430\u0437\u044B\u0432\u0430\u044E\u0442 \u0441\u043B\u0435\u0434\u0443\u044E\u0449\u0435\u0435 \u0442\u043E\u0436\u0434\u0435\u0441\u0442\u0432\u043E: \u0433\u0434\u0435 , \u2014 \u043F\u043E\u0441\u043B\u0435\u0434\u043E\u0432\u0430\u0442\u0435\u043B\u044C\u043D\u043E\u0441\u0442\u0438 , \u043F\u0440\u0438 \u044D\u0442\u043E\u043C \u0438 . \u042D\u0442\u043E \u043F\u0440\u0435\u043E\u0431\u0440\u0430\u0437\u043E\u0432\u0430\u043D\u0438\u0435 \u0431\u044B\u043B\u043E \u043D\u0430\u0437\u0432\u0430\u043D\u043E \u0432 \u0447\u0435\u0441\u0442\u044C \u043D\u043E\u0440\u0432\u0435\u0436\u0441\u043A\u043E\u0433\u043E \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0430 \u041D\u0438\u043B\u044C\u0441\u0430 \u0425\u0435\u043D\u0440\u0438\u043A\u0430 \u0410\u0431\u0435\u043B\u044F. \u0412 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0447\u0435\u0441\u043A\u043E\u043C \u0430\u043D\u0430\u043B\u0438\u0437\u0435 \u043E\u043D\u043E \u0438\u0441\u043F\u043E\u043B\u044C\u0437\u0443\u0435\u0442\u0441\u044F \u043F\u0440\u0438 \u0434\u043E\u043A\u0430\u0437\u0430\u0442\u0435\u043B\u044C\u0441\u0442\u0432\u0435 \u043F\u0440\u0438\u0437\u043D\u0430\u043A\u0430 \u0441\u0445\u043E\u0434\u0438\u043C\u043E\u0441\u0442\u0438 \u0414\u0438\u0440\u0438\u0445\u043B\u0435. \u041F\u0440\u0435\u043E\u0431\u0440\u0430\u0437\u043E\u0432\u0430\u043D\u0438\u0435 \u0410\u0431\u0435\u043B\u044F \u044F\u0432\u043B\u044F\u0435\u0442\u0441\u044F \u0434\u0438\u0441\u043A\u0440\u0435\u0442\u043D\u044B\u043C \u0430\u043D\u0430\u043B\u043E\u0433\u043E\u043C \u0438\u043D\u0442\u0435\u0433\u0440\u0438\u0440\u043E\u0432\u0430\u043D\u0438\u044F \u043F\u043E \u0447\u0430\u0441\u0442\u044F\u043C \u0438 \u0438\u043D\u043E\u0433\u0434\u0430 \u043D\u0430\u0437\u044B\u0432\u0430\u0435\u0442\u0441\u044F \u0441\u0443\u043C\u043C\u0438\u0440\u043E\u0432\u0430\u043D\u0438\u0435\u043C \u043F\u043E \u0447\u0430\u0441\u0442\u044F\u043C."@ru . . . "\uC544\uBCA8 \uBCC0\uD658(-\u8B8A\u63DB, Abel transformation), \uB610\uB294 \uC544\uBCA8\uC758 \uBCF4\uC870\uC815\uB9AC(-\u88DC\u52A9\u5B9A\u7406, Abel's lemma), \uC544\uBCA8\uC758 \uBD80\uBD84\uD569 \uACF5\uC2DD(-\u90E8\u5206\u5408\u516C\u5F0F, Abel's partial summation formula)\uC740 \uB450 \uC218\uC5F4\uC758 \uD56D\uBCC4\uACF1\uC758 \uD569\uC744 \uACC4\uC0B0\uD558\uAE30 \uC704\uD55C \uBCC0\uD658\uBC95\uC774\uB2E4. \uC5D0\uC11C\uC758 \uC544\uBCA8 \uBCC0\uD658\uC740 \uC801\uBD84\uC5D0\uC11C\uC758 \uBD80\uBD84\uC801\uBD84\uACFC \uC720\uC0AC\uD558\uB2E4. \uB2D0\uC2A4 \uD5E8\uB9AC\uD06C \uC544\uBCA8\uC758 \uC774\uB984\uC774 \uBD99\uC5B4 \uC788\uB2E4."@ko . . . . . . . "\u0414\u0438\u0441\u043A\u0440\u0435\u0442\u043D\u043E\u0435 \u043F\u0440\u0435\u043E\u0431\u0440\u0430\u0437\u043E\u0432\u0430\u043D\u0438\u0435 \u0410\u0431\u0435\u043B\u044F"@ru . . . . . . . . . . . . . . "\u5206\u90E8\u6C42\u548C\u6CD5\uFF08\u82F1\u8A9E\uFF1ASummation by parts\uFF09\u4E5F\u53EB\u963F\u8D1D\u5C14\u53D8\u6362\uFF08\u82F1\u8A9E\uFF1AAbel transformation\uFF0C\u6709\u522B\u4E8EAbel transform\uFF09\u6216\u963F\u8D1D\u5C14\u5F15\u7406\uFF08\u82F1\u8A9E\uFF1AAbel's lemma\uFF09\u662F\u6C42\u548C\u7684\u4E00\u79CD\u65B9\u6CD5\u3002\u8BBE\u548C\u4E3A\u4E24\u4E2A\u6570\u5217\uFF0C\u5219\u6709 . \u5B83\u88AB\u7528\u6765\u8BC1\u660E\u79EF\u5206\u7B2C\u4E8C\u4E2D\u503C\u5B9A\u7406\u3002 \u5206\u90E8\u6C42\u548C\u516C\u5F0F\u4E5F\u53EF\u88AB\u5199\u6210\u6BD4\u8F83\u5BF9\u79F0\u7684\u65B9\u5F0F\uFF1A"@zh . "In mathematics, summation by parts transforms the summation of products of sequences into other summations, often simplifying the computation or (especially) estimation of certain types of sums. It is also called Abel's lemma or Abel transformation, named after Niels Henrik Abel who introduced it in 1826."@en . . "V matematice je Abelova sumace, pojmenovan\u00E1 po Nielsi Henriku Abelovi, p\u0159episem n-t\u00E9ho \u010Dlenu posloupnosti na rozd\u00EDl dvou po sob\u011B jdouc\u00EDch \u010Dlenech sou\u010Dtov\u00E9 \u0159ady dan\u00E9 touto posloupnost\u00ED."@cs . . "V matematice je Abelova sumace, pojmenovan\u00E1 po Nielsi Henriku Abelovi, p\u0159episem n-t\u00E9ho \u010Dlenu posloupnosti na rozd\u00EDl dvou po sob\u011B jdouc\u00EDch \u010Dlenech sou\u010Dtov\u00E9 \u0159ady dan\u00E9 touto posloupnost\u00ED."@cs . . "\u5206\u90E8\u6C42\u548C\u6CD5"@zh . . "9451"^^ . . . . "\uC544\uBCA8 \uBCC0\uD658(-\u8B8A\u63DB, Abel transformation), \uB610\uB294 \uC544\uBCA8\uC758 \uBCF4\uC870\uC815\uB9AC(-\u88DC\u52A9\u5B9A\u7406, Abel's lemma), \uC544\uBCA8\uC758 \uBD80\uBD84\uD569 \uACF5\uC2DD(-\u90E8\u5206\u5408\u516C\u5F0F, Abel's partial summation formula)\uC740 \uB450 \uC218\uC5F4\uC758 \uD56D\uBCC4\uACF1\uC758 \uD569\uC744 \uACC4\uC0B0\uD558\uAE30 \uC704\uD55C \uBCC0\uD658\uBC95\uC774\uB2E4. \uC5D0\uC11C\uC758 \uC544\uBCA8 \uBCC0\uD658\uC740 \uC801\uBD84\uC5D0\uC11C\uC758 \uBD80\uBD84\uC801\uBD84\uACFC \uC720\uC0AC\uD558\uB2E4. \uB2D0\uC2A4 \uD5E8\uB9AC\uD06C \uC544\uBCA8\uC758 \uC774\uB984\uC774 \uBD99\uC5B4 \uC788\uB2E4."@ko . "1064141853"^^ . "En math\u00E9matiques, la formule de sommation par parties (parfois appel\u00E9e transformation d'Abel ou sommation d'Abel) permet de transformer une somme d'un produit de suites finies en d'autres sommes, simplifiant souvent le calcul et permettant l'estimation de certains types de sommes. C'est un analogue discret de l'int\u00E9gration par parties. Elle est \u00E0 la base du crit\u00E8re d'Abel permettant d'obtenir la semi-convergence de certaines s\u00E9ries."@fr . . . "In der Mathematik ist die abelsche partielle Summation (nach N. H. Abel) eine bestimmte Umformung einer Summe von Produkten jeweils zweier Zahlen."@de . "In matematica, la sommazione per parti, anche chiamata trasformazione (o lemma) di Abel, \u00E8 un procedimento che permette di scrivere in un altro modo la somma (finita o infinita) del prodotto di due successioni, consentendo cos\u00EC di avere una stima sul comportamento della serie in termini di convergenza."@it . "Partiell summation"@sv . . "\u0414\u0438\u0441\u043A\u0440\u0435\u0442\u043D\u0435 \u043F\u0435\u0440\u0435\u0442\u0432\u043E\u0440\u0435\u043D\u043D\u044F \u0410\u0431\u0435\u043B\u044F"@uk . . . . "Przekszta\u0142cenie Abela"@pl . "In matematica, la sommazione per parti, anche chiamata trasformazione (o lemma) di Abel, \u00E8 un procedimento che permette di scrivere in un altro modo la somma (finita o infinita) del prodotto di due successioni, consentendo cos\u00EC di avere una stima sul comportamento della serie in termini di convergenza."@it . "Partiell summation \u00E4r inom matematik en formel f\u00F6r att omvandla summor av produkter till en ofta mer l\u00E4tthanterlig form. Formeln kallas ibland f\u00F6r Abels lemma eller Abeltransformation och kan liknas med partiell integration."@sv . . . . "Przekszta\u0142cenie Abela (to\u017Csamo\u015B\u0107 Abela) \u2013 to\u017Csamo\u015B\u0107 algebraiczna zachodz\u0105ca dla sko\u0144czonych ci\u0105g\u00F3w liczbowych (b\u0105d\u017A og\u00F3lniej, element\u00F3w pier\u015Bcienia przemiennego). Niech b\u0119d\u0105 ci\u0105gami liczbowymi. Oznaczmy W\u00F3wczas zachodzi wz\u00F3r: W szczeg\u00F3lno\u015Bci, gdy"@pl . "Summation by parts"@en . . "En math\u00E9matiques, la formule de sommation par parties (parfois appel\u00E9e transformation d'Abel ou sommation d'Abel) permet de transformer une somme d'un produit de suites finies en d'autres sommes, simplifiant souvent le calcul et permettant l'estimation de certains types de sommes. C'est un analogue discret de l'int\u00E9gration par parties. Elle est \u00E0 la base du crit\u00E8re d'Abel permettant d'obtenir la semi-convergence de certaines s\u00E9ries."@fr . . . . "Abelova sumace"@cs . . . . "Partiell summation \u00E4r inom matematik en formel f\u00F6r att omvandla summor av produkter till en ofta mer l\u00E4tthanterlig form. Formeln kallas ibland f\u00F6r Abels lemma eller Abeltransformation och kan liknas med partiell integration."@sv . . "Sommazione per parti"@it . . "\u6570\u5B66\u306B\u304A\u3051\u308B\u90E8\u5206\u548C\u5206\uFF08\u3076\u3076\u3093\u308F\u3076\u3093\u3001\u82F1: summation by parts\uFF09\u306F\u3001\u7A4D\u306E\u548C\u5206\u3092\u8A08\u7B97\u3042\u308B\u3044\u306F\u8A55\u4FA1\u3057\u3084\u3059\u3044\u7279\u5B9A\u306E\u5F62\u306B\u5909\u5F62\u3059\u308B\u65B9\u6CD5\u306E\u4E00\u7A2E\u3067\u3042\u308B\u3002\u6570\u5217\u306E\u5B9A\u548C\u5206\u306B\u95A2\u3059\u308B\u90E8\u5206\u548C\u5206\u6CD5\u306F\u30CB\u30FC\u30EB\u30B9\u30FB\u30A2\u30FC\u30D9\u30EB\u306B\u56E0\u3093\u3067\u30A2\u30FC\u30D9\u30EB\u306E\u88DC\u984C\u3042\u308B\u3044\u306F\u30A2\u30FC\u30D9\u30EB\u306E\u7D1A\u6570\u5909\u5F62\u6CD5\u3068\u3082\u547C\u3070\u308C\u308B\u3002"@ja . . . . "\u6570\u5B66\u306B\u304A\u3051\u308B\u90E8\u5206\u548C\u5206\uFF08\u3076\u3076\u3093\u308F\u3076\u3093\u3001\u82F1: summation by parts\uFF09\u306F\u3001\u7A4D\u306E\u548C\u5206\u3092\u8A08\u7B97\u3042\u308B\u3044\u306F\u8A55\u4FA1\u3057\u3084\u3059\u3044\u7279\u5B9A\u306E\u5F62\u306B\u5909\u5F62\u3059\u308B\u65B9\u6CD5\u306E\u4E00\u7A2E\u3067\u3042\u308B\u3002\u6570\u5217\u306E\u5B9A\u548C\u5206\u306B\u95A2\u3059\u308B\u90E8\u5206\u548C\u5206\u6CD5\u306F\u30CB\u30FC\u30EB\u30B9\u30FB\u30A2\u30FC\u30D9\u30EB\u306B\u56E0\u3093\u3067\u30A2\u30FC\u30D9\u30EB\u306E\u88DC\u984C\u3042\u308B\u3044\u306F\u30A2\u30FC\u30D9\u30EB\u306E\u7D1A\u6570\u5909\u5F62\u6CD5\u3068\u3082\u547C\u3070\u308C\u308B\u3002"@ja . "\u90E8\u5206\u548C\u5206"@ja . . . "\u041F\u0435\u0440\u0435\u0442\u0432\u043E\u0440\u0435\u043D\u043D\u044F \u0410\u0431\u0435\u043B\u044F \u0454 \u0434\u0438\u0441\u043A\u0440\u0435\u0442\u043D\u0438\u043C \u0430\u043D\u0430\u043B\u043E\u0433\u043E\u043C \u0456\u043D\u0442\u0435\u0433\u0440\u0443\u0432\u0430\u043D\u043D\u044F \u0447\u0430\u0441\u0442\u0438\u043D\u0430\u043C\u0438 \u0456 \u0442\u0430\u043A\u043E\u0436 \u0456\u043D\u043E\u0434\u0456 \u043D\u0430\u0437\u0438\u0432\u0430\u0454\u0442\u044C\u0441\u044F \u0441\u0443\u043C\u0443\u0432\u0430\u043D\u043D\u044F\u043C \u0447\u0430\u0441\u0442\u0438\u043D\u0430\u043C\u0438. \u041F\u0435\u0440\u0435\u0442\u0432\u043E\u0440\u0435\u043D\u043D\u044F \u0448\u0438\u0440\u043E\u043A\u043E \u0432\u0438\u043A\u043E\u0440\u0438\u0441\u0442\u043E\u0432\u0443\u0454\u0442\u044C\u0441\u044F \u0443 \u0442\u0435\u043E\u0440\u0456\u0457 \u0440\u044F\u0434\u0456\u0432 \u0434\u043B\u044F \u0434\u043E\u0441\u043B\u0456\u0434\u0436\u0435\u043D\u043D\u044F \u0437\u0431\u0456\u0436\u043D\u043E\u0441\u0442\u0456 \u0440\u044F\u0434\u0456\u0432, \u043D\u0430\u043F\u0440\u0438\u043A\u043B\u0430\u0434 \u043F\u0440\u0438 \u0434\u043E\u0432\u0435\u0434\u0435\u043D\u043D\u0456 \u043E\u0437\u043D\u0430\u043A \u0410\u0431\u0435\u043B\u044F \u0456 \u0414\u0456\u0440\u0456\u0445\u043B\u0435."@uk . . "246188"^^ . . . . "Przekszta\u0142cenie Abela (to\u017Csamo\u015B\u0107 Abela) \u2013 to\u017Csamo\u015B\u0107 algebraiczna zachodz\u0105ca dla sko\u0144czonych ci\u0105g\u00F3w liczbowych (b\u0105d\u017A og\u00F3lniej, element\u00F3w pier\u015Bcienia przemiennego). Niech b\u0119d\u0105 ci\u0105gami liczbowymi. Oznaczmy W\u00F3wczas zachodzi wz\u00F3r: W szczeg\u00F3lno\u015Bci, gdy"@pl . . "\u5206\u90E8\u6C42\u548C\u6CD5\uFF08\u82F1\u8A9E\uFF1ASummation by parts\uFF09\u4E5F\u53EB\u963F\u8D1D\u5C14\u53D8\u6362\uFF08\u82F1\u8A9E\uFF1AAbel transformation\uFF0C\u6709\u522B\u4E8EAbel transform\uFF09\u6216\u963F\u8D1D\u5C14\u5F15\u7406\uFF08\u82F1\u8A9E\uFF1AAbel's lemma\uFF09\u662F\u6C42\u548C\u7684\u4E00\u79CD\u65B9\u6CD5\u3002\u8BBE\u548C\u4E3A\u4E24\u4E2A\u6570\u5217\uFF0C\u5219\u6709 . \u5B83\u88AB\u7528\u6765\u8BC1\u660E\u79EF\u5206\u7B2C\u4E8C\u4E2D\u503C\u5B9A\u7406\u3002 \u5206\u90E8\u6C42\u548C\u516C\u5F0F\u4E5F\u53EF\u88AB\u5199\u6210\u6BD4\u8F83\u5BF9\u79F0\u7684\u65B9\u5F0F\uFF1A"@zh . . "In mathematics, summation by parts transforms the summation of products of sequences into other summations, often simplifying the computation or (especially) estimation of certain types of sums. It is also called Abel's lemma or Abel transformation, named after Niels Henrik Abel who introduced it in 1826."@en . "Sommation par parties"@fr . . . . "\u041F\u0435\u0440\u0435\u0442\u0432\u043E\u0440\u0435\u043D\u043D\u044F \u0410\u0431\u0435\u043B\u044F \u0454 \u0434\u0438\u0441\u043A\u0440\u0435\u0442\u043D\u0438\u043C \u0430\u043D\u0430\u043B\u043E\u0433\u043E\u043C \u0456\u043D\u0442\u0435\u0433\u0440\u0443\u0432\u0430\u043D\u043D\u044F \u0447\u0430\u0441\u0442\u0438\u043D\u0430\u043C\u0438 \u0456 \u0442\u0430\u043A\u043E\u0436 \u0456\u043D\u043E\u0434\u0456 \u043D\u0430\u0437\u0438\u0432\u0430\u0454\u0442\u044C\u0441\u044F \u0441\u0443\u043C\u0443\u0432\u0430\u043D\u043D\u044F\u043C \u0447\u0430\u0441\u0442\u0438\u043D\u0430\u043C\u0438. \u041F\u0435\u0440\u0435\u0442\u0432\u043E\u0440\u0435\u043D\u043D\u044F \u0448\u0438\u0440\u043E\u043A\u043E \u0432\u0438\u043A\u043E\u0440\u0438\u0441\u0442\u043E\u0432\u0443\u0454\u0442\u044C\u0441\u044F \u0443 \u0442\u0435\u043E\u0440\u0456\u0457 \u0440\u044F\u0434\u0456\u0432 \u0434\u043B\u044F \u0434\u043E\u0441\u043B\u0456\u0434\u0436\u0435\u043D\u043D\u044F \u0437\u0431\u0456\u0436\u043D\u043E\u0441\u0442\u0456 \u0440\u044F\u0434\u0456\u0432, \u043D\u0430\u043F\u0440\u0438\u043A\u043B\u0430\u0434 \u043F\u0440\u0438 \u0434\u043E\u0432\u0435\u0434\u0435\u043D\u043D\u0456 \u043E\u0437\u043D\u0430\u043A \u0410\u0431\u0435\u043B\u044F \u0456 \u0414\u0456\u0440\u0456\u0445\u043B\u0435."@uk . . "\uC544\uBCA8 \uBCC0\uD658"@ko . . . . . "In der Mathematik ist die abelsche partielle Summation (nach N. H. Abel) eine bestimmte Umformung einer Summe von Produkten jeweils zweier Zahlen."@de . .