. . . . . . . . "Constante de Gelfond"@es . "Inom matematiken \u00E4r Gelfonds konstant den matematiska konstanten e\u03C0, det vill s\u00E4ga e upph\u00F6jt till \u03C0. Konstanten \u00E4r uppkallad efter den ryske matematikern Alexander Gelfond. Talet \u00E4r transcendent, precis som e och \u03C0 f\u00F6r sig, vilket f\u00F6ljer av att Eftersom \u2212i \u00E4r algebraiskt men inte rationellt \u00E4r e\u03C0 enligt Gelfonds sats transcendent. Konstanten omn\u00E4mns i Hilberts sjunde problem. Talet har decimalbr\u00E5ksutvecklingen (talf\u00F6ljd i OEIS) 23,1406926327792690057290863... och kedjebr\u00E5ksutvecklingen (talf\u00F6ljd i OEIS) [23, 7, 9, 3, 1, 1, 591, 2, 9, 1, 2, 23, ...]. Om man definierar och snabbt mot e\u03C0."@sv . . . "La costante di Gel'fond \u00E8 un numero trascendente definito come e elevato alla \u03C0, Prende il nome dal matematico Aleksandr Osipovi\u010D Gel'fond, che nel 1934 ne prov\u00F2 la trascendenza come conseguenza del suo teorema di Gel'fond. La sua espansione in frazione continua \u00E8"@it . "\u0641\u064A \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0627\u062A, \u062B\u0627\u0628\u062A\u0629 \u063A\u064A\u0644\u0641\u0648\u0646\u062F \u0647\u064A e\u03C0. \u0633\u0645\u064A\u062A \u0647\u0643\u0630\u0627 \u0646\u0633\u0628\u0629 \u0625\u0644\u0649 \u0623\u0644\u0643\u0633\u0646\u062F\u0631 \u063A\u064A\u0644\u0641\u0648\u0646\u062F."@ar . . . . . . . . "1114516442"^^ . . "En math\u00E9matiques, la constante de Gelfond est le nombre r\u00E9el transcendant e\u03C0, c'est-\u00E0-dire e \u00E0 la puissance \u03C0. Sa transcendance fut d\u00E9montr\u00E9e en 1929 par Alexandre Gelfond. C'est un cas particulier de son th\u00E9or\u00E8me de 1934. En effet, les nombres \u20131 (diff\u00E9rent de 0 et 1) et \u2013i (non rationnel) sont alg\u00E9briques, or (En effet, e\u03C0 = ei\u03C0\u00D7(\u2013i) et ei\u03C0 = \u20131). Cette constante fut mentionn\u00E9e dans le septi\u00E8me probl\u00E8me de Hilbert. Une constante reli\u00E9e est la constante de Gelfond-Schneider, 2\u221A2."@fr . "\u30B2\u30EB\u30D5\u30A9\u30F3\u30C8\u306E\u5B9A\u6570"@ja . "Se llama constante de Gelfond al n\u00FAmero , o sea, el n\u00FAmero e elevado al n\u00FAmero \u03C0. Establecer si este n\u00FAmero es trascendente o no fue uno de los 23 problemas que Hilbert propuso como especialmente importantes en el Congreso Internacional de Matem\u00E1ticos de 1900 en Par\u00EDs. Que este n\u00FAmero es trascendente (y por tanto, irracional) fue demostrado por Gelfond en 1934. Otra de las constantes relacionadas con esta es , conocida como constante de Gelfond-Schneider. El valor de la constante de Gelfond es Su valor puede hallarse mediante la f\u00F3rmula recurrente con Una vez llegado al t\u00E9rmino deseado, basta tomar:"@es . . . . . "Costante di Gel'fond"@it . . . . . "Het getal , oftewel e tot de macht , wordt de constante van Gelfond genoemd. De numerieke waarde bedraagt bij benadering 23,1406926... De constante kan ook geschreven worden als: , waarin de imaginaire eenheid is. Definieert men en voor , dan convergeert snel naar ."@nl . "\u041F\u043E\u0441\u0442\u043E\u044F\u043D\u043D\u0430\u044F \u0413\u0435\u043B\u044C\u0444\u043E\u043D\u0434\u0430"@ru . . . . . "Constant de Gelfond"@ca . . . . . "1984963"^^ . . . . . . . . . . . "En matem\u00E0tiques, la constant de Gelfond \u00E9s un nombre transcendent definit com el nombre d'Euler e elevat al nombre pi \u03C0: T\u00E9 aquest nom en honor del matem\u00E0tic rus Alexander Gelfond que el 1934 va provar-ne la transcend\u00E8ncia mitjan\u00E7ant el teorema de Gelfond-Schneider. La seva fracci\u00F3 cont\u00EDnua no \u00E9s ni finita ni per\u00EC\u00F2dica i \u00E9s , \u00E9s a dir:"@ca . . . . . "Gelfonds konstant"@sv . . "\u53C8\u7A31\u683C\u723E\u8C50\u5FB7\u5E38\u6578\uFF08\u82F1\u8A9E\uFF1AGelfond's constant\uFF09\u662F\u4E00\u4E2A\u6570\u5B66\u5E38\u6570\u3002\u4E0Ee\u548C\u03C0\u4E00\u6837\uFF0C\u5B83\u662F\u4E00\u4E2A\u8D85\u8D8A\u6570\u3002\u8FD9\u53EF\u4EE5\u7528\u683C\u5C14\u4E30\u5FB7-\u65BD\u5948\u5FB7\u5B9A\u7406\u6765\u8BC1\u660E\uFF0C\u5E76\u6CE8\u610F\u5230\uFF1A \u5176\u4E2Di\u662F\u865A\u6570\u5355\u4F4D\u3002\u7531\u4E8E\u2212i\u662F\u4EE3\u6570\u6570\uFF0C\u4F46\u80AF\u5B9A\u4E0D\u662F\u6709\u7406\u6570\uFF0C\u56E0\u6B64e\u03C0\u662F\u8D85\u8D8A\u6570\u3002\u8FD9\u4E2A\u5E38\u6570\u5728\u5E0C\u5C14\u4F2F\u7279\u7B2C\u4E03\u95EE\u9898\u4E2D\u66FE\u63D0\u5230\u8FC7\u3002\u4E00\u4E2A\u76F8\u5173\u7684\u5E38\u6570\u662F\uFF0C\u53C8\u79F0\u4E3A\u683C\u5C14\u4E30\u5FB7-\u65BD\u5948\u5FB7\u5E38\u6570\u3002\u76F8\u5173\u7684\u503C\u4E5F\u662F\u65E0\u7406\u6570\u3002"@zh . "Em matem\u00E1tica, a constante de Gelfond, nomeada em mem\u00F3ria de Alexander Gelfond, \u00E9 e\u03C0, isto \u00E9, e na pot\u00EAncia \u03C0. Assim como e e \u03C0, esta constante \u00E9 um n\u00FAmero transcendental. Isto foi estabelecido a primeira vez por Gelfond e pode atualmente ser considerado uma aplica\u00E7\u00E3o do teorema de Gelfond-Schneider, observando que sendo i a unidade imagin\u00E1ria. Como \u2212i \u00E9 alg\u00E9brico, mas certamente n\u00E3o racional, e\u03C0 \u00E9 transcendental. A constante foi mencionada no s\u00E9timo problema de Hilbert. Uma constante relacionada \u00E9 , conhecida como . O valor relacionado \u03C0 + e\u03C0 \u00E9 tamb\u00E9m irracional."@pt . . . . "Constante de Gelfond"@fr . "Constante van Gelfond"@nl . . . . . . "\u0641\u064A \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0627\u062A, \u062B\u0627\u0628\u062A\u0629 \u063A\u064A\u0644\u0641\u0648\u0646\u062F \u0647\u064A e\u03C0. \u0633\u0645\u064A\u062A \u0647\u0643\u0630\u0627 \u0646\u0633\u0628\u0629 \u0625\u0644\u0649 \u0623\u0644\u0643\u0633\u0646\u062F\u0631 \u063A\u064A\u0644\u0641\u0648\u0646\u062F."@ar . . . "Se llama constante de Gelfond al n\u00FAmero , o sea, el n\u00FAmero e elevado al n\u00FAmero \u03C0. Establecer si este n\u00FAmero es trascendente o no fue uno de los 23 problemas que Hilbert propuso como especialmente importantes en el Congreso Internacional de Matem\u00E1ticos de 1900 en Par\u00EDs. Que este n\u00FAmero es trascendente (y por tanto, irracional) fue demostrado por Gelfond en 1934. Otra de las constantes relacionadas con esta es , conocida como constante de Gelfond-Schneider. El valor de la constante de Gelfond es Su valor puede hallarse mediante la f\u00F3rmula recurrente con"@es . "In mathematics, Gelfond's constant, named after Aleksandr Gelfond, is e\u03C0, that is, e raised to the power \u03C0. Like both e and \u03C0, this constant is a transcendental number. This was first established by Gelfond and may now be considered as an application of the Gelfond\u2013Schneider theorem, noting that where i is the imaginary unit. Since \u2212i is algebraic but not rational, e\u03C0 is transcendental. The constant was mentioned in Hilbert's seventh problem. A related constant is 2\u221A2, known as the Gelfond\u2013Schneider constant. The related value \u03C0 + e\u03C0 is also irrational."@en . . "\uC790\uC5F0\uB85C\uADF8\uC758 \uBC11 \uC758 \uC6D0\uC8FC\uC728 \uC81C\uACF1 \uC740 23\uACFC 24 \uC0AC\uC774\uC758 \uC2E4\uC218\uC774\uBA70, \uAC94\uD3F0\uD2B8-\uC288\uB098\uC774\uB354 \uC815\uB9AC\uB97C \uC0AC\uC6A9\uD558\uC5EC \uCD08\uC6D4\uC218\uC784\uC744 \uBCF4\uC77C \uC218 \uC788\uB2E4."@ko . . . . . . "En matem\u00E0tiques, la constant de Gelfond \u00E9s un nombre transcendent definit com el nombre d'Euler e elevat al nombre pi \u03C0: T\u00E9 aquest nom en honor del matem\u00E0tic rus Alexander Gelfond que el 1934 va provar-ne la transcend\u00E8ncia mitjan\u00E7ant el teorema de Gelfond-Schneider. La seva fracci\u00F3 cont\u00EDnua no \u00E9s ni finita ni per\u00EC\u00F2dica i \u00E9s , \u00E9s a dir:"@ca . . . . "Inom matematiken \u00E4r Gelfonds konstant den matematiska konstanten e\u03C0, det vill s\u00E4ga e upph\u00F6jt till \u03C0. Konstanten \u00E4r uppkallad efter den ryske matematikern Alexander Gelfond. Talet \u00E4r transcendent, precis som e och \u03C0 f\u00F6r sig, vilket f\u00F6ljer av att Eftersom \u2212i \u00E4r algebraiskt men inte rationellt \u00E4r e\u03C0 enligt Gelfonds sats transcendent. Konstanten omn\u00E4mns i Hilberts sjunde problem. Talet har decimalbr\u00E5ksutvecklingen (talf\u00F6ljd i OEIS) 23,1406926327792690057290863... och kedjebr\u00E5ksutvecklingen (talf\u00F6ljd i OEIS) [23, 7, 9, 3, 1, 1, 591, 2, 9, 1, 2, 23, ...]. Om man definierar och f\u00F6r n > 0, d\u00E5 konvergerar sekvensen snabbt mot e\u03C0."@sv . . . "Gelfond's constant"@en . . "\u30B2\u30EB\u30D5\u30A9\u30F3\u30C8\u306E\u5B9A\u6570\uFF08\u30B2\u30EB\u30D5\u30A9\u30F3\u30C8\u306E\u3066\u3044\u3059\u3046\u3001\u82F1\u8A9E: Gelfond's constant\uFF09\u306F\u6570\u5B66\u5B9A\u6570\u306E\u4E00\u3064\u3067\u3001\u30CD\u30A4\u30D4\u30A2\u6570 e \u3068\u5186\u5468\u7387 \u03C0 \u3092\u7528\u3044\u3066 e\u03C0 \u3068\u8868\u3055\u308C\u308B\u6570\u3067\u3042\u308B\u3002\u5C0F\u6570\u8868\u793A\u306F e\u03C0 = 23.14069 26327 79269 00572 90863 67948 54738 02661 06242 60021 19934 45046 40952 43423 50690 45278 35169 71997 06754 92196 76\u2026 (\u30AA\u30F3\u30E9\u30A4\u30F3\u6574\u6570\u5217\u5927\u8F9E\u5178\u306E\u6570\u5217 A039661) \u3067\u3042\u308B\u3002\u3053\u306E\u6570\u306F\u30ED\u30B7\u30A2\u306E\u6570\u5B66\u8005\u306B\u3061\u306A\u3093\u3067\u540D\u4ED8\u3051\u3089\u308C\u305F\u3002\u30B2\u30EB\u30D5\u30A9\u30F3\u30C8\u306E\u5B9A\u6570\u306F e \u3084 \u03C0 \u3068\u540C\u69D8\u306B\u8D85\u8D8A\u6570\u3067\u3042\u308B\u3002\u3053\u306E\u3053\u3068\u306F\u30B2\u30EB\u30D5\u30A9\u30F3\u30C8\uFF1D\u30B7\u30E5\u30CA\u30A4\u30C0\u30FC\u306E\u5B9A\u7406\u304B\u3089\u8A3C\u660E\u3067\u304D\u308B\u3002"@ja . . "E\u7684\u03C0\u6B21\u65B9"@zh . "\u062B\u0627\u0628\u062A\u0629 \u063A\u064A\u0644\u0641\u0648\u0646\u062F"@ar . "\uC790\uC5F0\uB85C\uADF8\uC758 \uBC11 \uC758 \uC6D0\uC8FC\uC728 \uC81C\uACF1 \uC740 23\uACFC 24 \uC0AC\uC774\uC758 \uC2E4\uC218\uC774\uBA70, \uAC94\uD3F0\uD2B8-\uC288\uB098\uC774\uB354 \uC815\uB9AC\uB97C \uC0AC\uC6A9\uD558\uC5EC \uCD08\uC6D4\uC218\uC784\uC744 \uBCF4\uC77C \uC218 \uC788\uB2E4."@ko . . . . . . . "\u30B2\u30EB\u30D5\u30A9\u30F3\u30C8\u306E\u5B9A\u6570\uFF08\u30B2\u30EB\u30D5\u30A9\u30F3\u30C8\u306E\u3066\u3044\u3059\u3046\u3001\u82F1\u8A9E: Gelfond's constant\uFF09\u306F\u6570\u5B66\u5B9A\u6570\u306E\u4E00\u3064\u3067\u3001\u30CD\u30A4\u30D4\u30A2\u6570 e \u3068\u5186\u5468\u7387 \u03C0 \u3092\u7528\u3044\u3066 e\u03C0 \u3068\u8868\u3055\u308C\u308B\u6570\u3067\u3042\u308B\u3002\u5C0F\u6570\u8868\u793A\u306F e\u03C0 = 23.14069 26327 79269 00572 90863 67948 54738 02661 06242 60021 19934 45046 40952 43423 50690 45278 35169 71997 06754 92196 76\u2026 (\u30AA\u30F3\u30E9\u30A4\u30F3\u6574\u6570\u5217\u5927\u8F9E\u5178\u306E\u6570\u5217 A039661) \u3067\u3042\u308B\u3002\u3053\u306E\u6570\u306F\u30ED\u30B7\u30A2\u306E\u6570\u5B66\u8005\u306B\u3061\u306A\u3093\u3067\u540D\u4ED8\u3051\u3089\u308C\u305F\u3002\u30B2\u30EB\u30D5\u30A9\u30F3\u30C8\u306E\u5B9A\u6570\u306F e \u3084 \u03C0 \u3068\u540C\u69D8\u306B\u8D85\u8D8A\u6570\u3067\u3042\u308B\u3002\u3053\u306E\u3053\u3068\u306F\u30B2\u30EB\u30D5\u30A9\u30F3\u30C8\uFF1D\u30B7\u30E5\u30CA\u30A4\u30C0\u30FC\u306E\u5B9A\u7406\u304B\u3089\u8A3C\u660E\u3067\u304D\u308B\u3002"@ja . . . . "Em matem\u00E1tica, a constante de Gelfond, nomeada em mem\u00F3ria de Alexander Gelfond, \u00E9 e\u03C0, isto \u00E9, e na pot\u00EAncia \u03C0. Assim como e e \u03C0, esta constante \u00E9 um n\u00FAmero transcendental. Isto foi estabelecido a primeira vez por Gelfond e pode atualmente ser considerado uma aplica\u00E7\u00E3o do teorema de Gelfond-Schneider, observando que sendo i a unidade imagin\u00E1ria. Como \u2212i \u00E9 alg\u00E9brico, mas certamente n\u00E3o racional, e\u03C0 \u00E9 transcendental. A constante foi mencionada no s\u00E9timo problema de Hilbert. Uma constante relacionada \u00E9 , conhecida como . O valor relacionado \u03C0 + e\u03C0 \u00E9 tamb\u00E9m irracional."@pt . "9862"^^ . . "\u041F\u043E\u0441\u0442\u043E\u044F\u043D\u043D\u0430\u044F \u0413\u0435\u043B\u044C\u0444\u043E\u043D\u0434\u0430 \u2014 \u0442\u0440\u0430\u043D\u0441\u0446\u0435\u043D\u0434\u0435\u043D\u0442\u043D\u043E\u0435 \u0447\u0438\u0441\u043B\u043E (\u0442\u043E \u0435\u0441\u0442\u044C e \u0432 \u0441\u0442\u0435\u043F\u0435\u043D\u0438 \u03C0). \u041D\u0430\u0437\u0432\u0430\u043D\u0430 \u0432 \u0447\u0435\u0441\u0442\u044C \u0410\u043B\u0435\u043A\u0441\u0430\u043D\u0434\u0440\u0430 \u041E\u0441\u0438\u043F\u043E\u0432\u0438\u0447\u0430 \u0413\u0435\u043B\u044C\u0444\u043E\u043D\u0434\u0430. \u0414\u043E\u043A\u0430\u0437\u0430\u0442\u0435\u043B\u044C\u0441\u0442\u0432\u043E \u0442\u0440\u0430\u043D\u0441\u0446\u0435\u043D\u0434\u0435\u043D\u0442\u043D\u043E\u0441\u0442\u0438 \u044D\u0442\u043E\u0433\u043E \u0447\u0438\u0441\u043B\u0430 \u2014 \u043E\u0434\u0438\u043D \u0438\u0437 \u043F\u0443\u043D\u043A\u0442\u043E\u0432 \u0441\u0435\u0434\u044C\u043C\u043E\u0439 \u043F\u0440\u043E\u0431\u043B\u0435\u043C\u044B \u0413\u0438\u043B\u044C\u0431\u0435\u0440\u0442\u0430."@ru . "Constante de Gelfond"@pt . . . . . . "\uC790\uC5F0\uB85C\uADF8\uC758 \uBC11\uC758 \uC6D0\uC8FC\uC728 \uC81C\uACF1"@ko . . . . "Het getal , oftewel e tot de macht , wordt de constante van Gelfond genoemd. De numerieke waarde bedraagt bij benadering 23,1406926... De constante kan ook geschreven worden als: , waarin de imaginaire eenheid is. Definieert men en voor , dan convergeert snel naar ."@nl . "In mathematics, Gelfond's constant, named after Aleksandr Gelfond, is e\u03C0, that is, e raised to the power \u03C0. Like both e and \u03C0, this constant is a transcendental number. This was first established by Gelfond and may now be considered as an application of the Gelfond\u2013Schneider theorem, noting that where i is the imaginary unit. Since \u2212i is algebraic but not rational, e\u03C0 is transcendental. The constant was mentioned in Hilbert's seventh problem. A related constant is 2\u221A2, known as the Gelfond\u2013Schneider constant. The related value \u03C0 + e\u03C0 is also irrational."@en . "\u53C8\u7A31\u683C\u723E\u8C50\u5FB7\u5E38\u6578\uFF08\u82F1\u8A9E\uFF1AGelfond's constant\uFF09\u662F\u4E00\u4E2A\u6570\u5B66\u5E38\u6570\u3002\u4E0Ee\u548C\u03C0\u4E00\u6837\uFF0C\u5B83\u662F\u4E00\u4E2A\u8D85\u8D8A\u6570\u3002\u8FD9\u53EF\u4EE5\u7528\u683C\u5C14\u4E30\u5FB7-\u65BD\u5948\u5FB7\u5B9A\u7406\u6765\u8BC1\u660E\uFF0C\u5E76\u6CE8\u610F\u5230\uFF1A \u5176\u4E2Di\u662F\u865A\u6570\u5355\u4F4D\u3002\u7531\u4E8E\u2212i\u662F\u4EE3\u6570\u6570\uFF0C\u4F46\u80AF\u5B9A\u4E0D\u662F\u6709\u7406\u6570\uFF0C\u56E0\u6B64e\u03C0\u662F\u8D85\u8D8A\u6570\u3002\u8FD9\u4E2A\u5E38\u6570\u5728\u5E0C\u5C14\u4F2F\u7279\u7B2C\u4E03\u95EE\u9898\u4E2D\u66FE\u63D0\u5230\u8FC7\u3002\u4E00\u4E2A\u76F8\u5173\u7684\u5E38\u6570\u662F\uFF0C\u53C8\u79F0\u4E3A\u683C\u5C14\u4E30\u5FB7-\u65BD\u5948\u5FB7\u5E38\u6570\u3002\u76F8\u5173\u7684\u503C\u4E5F\u662F\u65E0\u7406\u6570\u3002"@zh . "En math\u00E9matiques, la constante de Gelfond est le nombre r\u00E9el transcendant e\u03C0, c'est-\u00E0-dire e \u00E0 la puissance \u03C0. Sa transcendance fut d\u00E9montr\u00E9e en 1929 par Alexandre Gelfond. C'est un cas particulier de son th\u00E9or\u00E8me de 1934. En effet, les nombres \u20131 (diff\u00E9rent de 0 et 1) et \u2013i (non rationnel) sont alg\u00E9briques, or (En effet, e\u03C0 = ei\u03C0\u00D7(\u2013i) et ei\u03C0 = \u20131). Cette constante fut mentionn\u00E9e dans le septi\u00E8me probl\u00E8me de Hilbert. Une constante reli\u00E9e est la constante de Gelfond-Schneider, 2\u221A2."@fr . . "La costante di Gel'fond \u00E8 un numero trascendente definito come e elevato alla \u03C0, Prende il nome dal matematico Aleksandr Osipovi\u010D Gel'fond, che nel 1934 ne prov\u00F2 la trascendenza come conseguenza del suo teorema di Gel'fond. La sua espansione in frazione continua \u00E8"@it . "\u041F\u043E\u0441\u0442\u043E\u044F\u043D\u043D\u0430\u044F \u0413\u0435\u043B\u044C\u0444\u043E\u043D\u0434\u0430 \u2014 \u0442\u0440\u0430\u043D\u0441\u0446\u0435\u043D\u0434\u0435\u043D\u0442\u043D\u043E\u0435 \u0447\u0438\u0441\u043B\u043E (\u0442\u043E \u0435\u0441\u0442\u044C e \u0432 \u0441\u0442\u0435\u043F\u0435\u043D\u0438 \u03C0). \u041D\u0430\u0437\u0432\u0430\u043D\u0430 \u0432 \u0447\u0435\u0441\u0442\u044C \u0410\u043B\u0435\u043A\u0441\u0430\u043D\u0434\u0440\u0430 \u041E\u0441\u0438\u043F\u043E\u0432\u0438\u0447\u0430 \u0413\u0435\u043B\u044C\u0444\u043E\u043D\u0434\u0430. \u0414\u043E\u043A\u0430\u0437\u0430\u0442\u0435\u043B\u044C\u0441\u0442\u0432\u043E \u0442\u0440\u0430\u043D\u0441\u0446\u0435\u043D\u0434\u0435\u043D\u0442\u043D\u043E\u0441\u0442\u0438 \u044D\u0442\u043E\u0433\u043E \u0447\u0438\u0441\u043B\u0430 \u2014 \u043E\u0434\u0438\u043D \u0438\u0437 \u043F\u0443\u043D\u043A\u0442\u043E\u0432 \u0441\u0435\u0434\u044C\u043C\u043E\u0439 \u043F\u0440\u043E\u0431\u043B\u0435\u043C\u044B \u0413\u0438\u043B\u044C\u0431\u0435\u0440\u0442\u0430."@ru .