"Der Konvergenzradius ist in der Analysis eine Eigenschaft einer Potenzreihe der Form , die angibt, in welchem Bereich der reellen Gerade oder der komplexen Ebene f\u00FCr die Potenzreihe Konvergenz garantiert ist."@de . "Raggio di convergenza"@it . . "Polom\u011Br konvergence mocninn\u00E9 \u0159ady je v matematice polom\u011Br nejv\u011Bt\u0161\u00EDho kruhu, v n\u011Bm\u017E mocninn\u00E1 \u0159ada konverguje. Polom\u011Br konvergence je nez\u00E1porn\u00E9 re\u00E1ln\u00E9 \u010D\u00EDslo nebo . Je-li polom\u011Br konvergence kladn\u00FD, mocninn\u00E1 \u0159ada a rovnom\u011Brn\u011B na kompaktn\u00ED mno\u017Ein\u011B uvnit\u0159 otev\u0159en\u00E9ho kruhu s polom\u011Brem rovn\u00FDm polom\u011Bru konvergence a je Taylorovou \u0159adou analytick\u00E9 funkce, ke kter\u00E9 konverguje."@cs . . . . . "\u041A\u0440\u0443\u0433 \u0441\u0445\u043E\u0434\u0438\u043C\u043E\u0441\u0442\u0438 \u0441\u0442\u0435\u043F\u0435\u043D\u043D\u043E\u0433\u043E \u0440\u044F\u0434\u0430 \u2014 \u044D\u0442\u043E \u043A\u0440\u0443\u0433 \u0432\u0438\u0434\u0430 , , \u0432 \u043A\u043E\u0442\u043E\u0440\u043E\u043C \u0440\u044F\u0434 \u0430\u0431\u0441\u043E\u043B\u044E\u0442\u043D\u043E \u0441\u0445\u043E\u0434\u0438\u0442\u0441\u044F, \u0430 \u0432\u043D\u0435 \u0435\u0433\u043E, \u043F\u0440\u0438 , \u0440\u0430\u0441\u0445\u043E\u0434\u0438\u0442\u0441\u044F. \u0418\u043D\u044B\u043C\u0438 \u0441\u043B\u043E\u0432\u0430\u043C\u0438, \u043A\u0440\u0443\u0433 \u0441\u0445\u043E\u0434\u0438\u043C\u043E\u0441\u0442\u0438 \u0441\u0442\u0435\u043F\u0435\u043D\u043D\u043E\u0433\u043E \u0440\u044F\u0434\u0430 \u0435\u0441\u0442\u044C \u0432\u043D\u0443\u0442\u0440\u0435\u043D\u043D\u043E\u0441\u0442\u044C \u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432\u0430 \u0442\u043E\u0447\u0435\u043A \u0441\u0445\u043E\u0434\u0438\u043C\u043E\u0441\u0442\u0438 \u0440\u044F\u0434\u0430. \u041A\u0440\u0443\u0433 \u0441\u0445\u043E\u0434\u0438\u043C\u043E\u0441\u0442\u0438 \u043C\u043E\u0436\u0435\u0442 \u0432\u044B\u0440\u043E\u0436\u0434\u0430\u0442\u044C\u0441\u044F \u0432 \u043F\u0443\u0441\u0442\u043E\u0435 \u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432\u043E, \u043A\u043E\u0433\u0434\u0430 , \u0438 \u043C\u043E\u0436\u0435\u0442 \u0441\u043E\u0432\u043F\u0430\u0434\u0430\u0442\u044C \u0441\u043E \u0432\u0441\u0435\u0439 \u043F\u043B\u043E\u0441\u043A\u043E\u0441\u0442\u044C\u044E \u043F\u0435\u0440\u0435\u043C\u0435\u043D\u043D\u043E\u0433\u043E , \u043A\u043E\u0433\u0434\u0430 ."@ru . . . "Polom\u011Br konvergence mocninn\u00E9 \u0159ady je v matematice polom\u011Br nejv\u011Bt\u0161\u00EDho kruhu, v n\u011Bm\u017E mocninn\u00E1 \u0159ada konverguje. Polom\u011Br konvergence je nez\u00E1porn\u00E9 re\u00E1ln\u00E9 \u010D\u00EDslo nebo . Je-li polom\u011Br konvergence kladn\u00FD, mocninn\u00E1 \u0159ada a rovnom\u011Brn\u011B na kompaktn\u00ED mno\u017Ein\u011B uvnit\u0159 otev\u0159en\u00E9ho kruhu s polom\u011Brem rovn\u00FDm polom\u011Bru konvergence a je Taylorovou \u0159adou analytick\u00E9 funkce, ke kter\u00E9 konverguje."@cs . . . "Le rayon de convergence d'une s\u00E9rie enti\u00E8re est le nombre r\u00E9el positif ou +\u221E \u00E9gal \u00E0 la borne sup\u00E9rieure de l'ensemble des modules des nombres complexes o\u00F9 la s\u00E9rie converge (au sens classique de la convergence simple):"@fr . . . "Radio de convergencia"@es . . . "\u6536\u655B\u534A\u5F84"@zh . "En matem\u00E1ticas, seg\u00FAn el teorema de Cauchy-Hadamard, el radio de convergencia de una serie de la forma , con , viene dado por la expresi\u00F3n:"@es . "Le rayon de convergence d'une s\u00E9rie enti\u00E8re est le nombre r\u00E9el positif ou +\u221E \u00E9gal \u00E0 la borne sup\u00E9rieure de l'ensemble des modules des nombres complexes o\u00F9 la s\u00E9rie converge (au sens classique de la convergence simple):"@fr . . . . "\u0641\u064A \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0627\u062A\u060C \u0646\u0635\u0641 \u0642\u0637\u0631 \u0627\u0644\u062A\u0642\u0627\u0631\u0628 (\u0628\u0627\u0644\u0625\u0646\u062C\u0644\u064A\u0632\u064A\u0629: Radius of Convergence)\u200F \u0644\u0645\u062A\u0633\u0644\u0633\u0644\u0629 \u0642\u0648\u0649 \u0647\u0648 \u0646\u0635\u0641 \u0642\u0637\u0631 \u0623\u0643\u0628\u0631 \u0642\u0631\u0635 \u062A\u062A\u0642\u0627\u0631\u0628 \u0641\u064A\u0647 \u0627\u0644\u0645\u062A\u0633\u0644\u0633\u0644\u0629\u060C \u0648\u0647\u0648 \u0625\u0645\u0627 \u0639\u062F\u062F \u062D\u0642\u064A\u0642\u064A \u063A\u064A\u0631 \u0633\u0627\u0644\u0628 \u0623\u0648 \u221E. \u0648\u0641\u0642\u064B\u0627 \u0644\u0645\u0628\u0631\u0647\u0646\u0629 \u0643\u0648\u0634\u064A-\u0647\u0627\u062F\u0627\u0645\u0627\u0631\u060C \u062A\u0639\u0637\u0649 \u0646\u0635\u0641 \u0642\u0637\u0631 \u062A\u0642\u0627\u0631\u0628 \u0645\u062A\u0633\u0644\u0633\u0644\u0629 \u0645\u0646 \u0627\u0644\u0634\u0643\u0644 \u060C \u0645\u0639 \u060C \u0628\u0648\u0627\u0633\u0637\u0629 \u0627\u0644\u0639\u0628\u0627\u0631\u0629 \u0627\u0644\u062A\u0627\u0644\u064A\u0629: \u0625\u0630\u0627 \u0643\u0627\u0646 \u0646\u0635\u0641 \u0642\u0637\u0631 \u062A\u0642\u0627\u0631\u0628 \u0645\u062A\u0633\u0644\u0633\u0644\u0629 \u062F\u0627\u0644\u0629 \u0647\u0648 \u0645\u0627 \u0644\u0627 \u0646\u0647\u0627\u064A\u0629\u060C \u064A\u0645\u0643\u0646 \u0623\u0646 \u062A\u0645\u062F\u062F \u0627\u0644\u062F\u0627\u0644\u0629 \u0625\u0644\u0649 \u062F\u0627\u0644\u0629 \u0643\u0627\u0645\u0644\u0629."@ar . . . . . . . "\u53CE\u675F\u534A\u5F84(\u3057\u3085\u3046\u305D\u304F\u306F\u3093\u3051\u3044\u3001radius of convergence) \u3068\u306F\u3001\u51AA\u7D1A\u6570\u304C\u53CE\u675F\u3059\u308B\u5B9A\u7FA9\u57DF\u3092\u4E0E\u3048\u308B\u975E\u8CA0\u91CF\uFF08\u5B9F\u6570\u3042\u308B\u3044\u306F\u221E\uFF09\u3067\u3042\u308B\u3002 \u6B21\u306E\u51AA\u7D1A\u6570\u3092\u8003\u3048\u308B\u3002 \u305F\u3060\u3057\u3001\u4E2D\u5FC3 a \u3084\u4FC2\u6570 cn \u306F\u8907\u7D20\u6570\uFF08\u7279\u306B\u5B9F\u6570\uFF09\u3068\u3059\u308B\u3002\u6B21\u306E\u6761\u4EF6\u304C\u6210\u7ACB\u3059\u308B\u3068\u304D\u3001 r \u3092\u3053\u306E\u7D1A\u6570\u306E\u53CE\u675F\u534A\u5F84\u3068\u3044\u3046\u3002 \u3067\u3042\u308B\u3068\u304D\u3001\u7D1A\u6570\u306F\u53CE\u675F\u3057\u3001 \u3067\u3042\u308B\u3068\u304D\u3001\u7D1A\u6570\u306F\u767A\u6563\u3059\u308B\u3002 \u3082\u3057\u3001\u7D1A\u6570\u304C\u5168\u3066\u306E\u8907\u7D20\u6570 z \u306B\u95A2\u3057\u3066\u53CE\u675F\u3059\u308B\u306A\u3089\u3070\u3001\u53CE\u675F\u534A\u5F84\u306F \u221E \u3068\u306A\u308B\u3002"@ja . . "\u6536\u655B\u534A\u5F84\u662F\u6570\u5B66\u5206\u6790\u4E2D\u4E0E\u5E42\u7EA7\u6570\u6709\u5173\u7684\u6982\u5FF5\u3002\u4E00\u4E2A\u5E42\u7EA7\u6570\u7684\u6536\u655B\u534A\u5F84\u662F\u4E00\u4E2A\u975E\u8D1F\u7684\u6269\u5C55\u5B9E\u6570\uFF08\u5305\u62EC\u65E0\u7A77\u5927\uFF09\u3002\u6536\u655B\u534A\u5F84\u8868\u793A\u5E42\u7EA7\u6570\u6536\u655B\u7684\u8303\u56F4\u3002\u5728\u6536\u655B\u534A\u5F84\u5185\u7684\u7D27\u96C6\u4E0A\uFF0C\u5E42\u7EA7\u6570\u5BF9\u5E94\u7684\u51FD\u6570\u4E00\u81F4\u6536\u655B\uFF0C\u5E76\u4E14\u5E42\u7EA7\u6570\u5C31\u662F\u6B64\u51FD\u6570\u5C55\u5F00\u5F97\u5230\u7684\u6CF0\u52D2\u7EA7\u6570\u3002\u4F46\u662F\uFF0C\u5728\u6536\u655B\u534A\u5F84\u4E0A\u5E42\u7EA7\u6570\u7684\u655B\u6563\u6027\u662F\u4E0D\u786E\u5B9A\u7684\u3002"@zh . . . . "In mathematics, the radius of convergence of a power series is the radius of the largest disk at the center of the series in which the series converges. It is either a non-negative real number or . When it is positive, the power series converges absolutely and uniformly on compact sets inside the open disk of radius equal to the radius of convergence, and it is the Taylor series of the analytic function to which it converges. In case of multiple singularities of a function (singularities are those values of the argument for which the function is not defined), the radius of convergence is the shortest or minimum of all the respective distances (which are all non-negative numbers) calculated from the center of the disk of convergence to the respective singularities of the function."@en . . . . . . . "Konvergenzradius"@de . "\u041A\u0440\u0443\u0433 \u0441\u0445\u043E\u0434\u0438\u043C\u043E\u0441\u0442\u0438"@ru . "\u0641\u064A \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0627\u062A\u060C \u0646\u0635\u0641 \u0642\u0637\u0631 \u0627\u0644\u062A\u0642\u0627\u0631\u0628 (\u0628\u0627\u0644\u0625\u0646\u062C\u0644\u064A\u0632\u064A\u0629: Radius of Convergence)\u200F \u0644\u0645\u062A\u0633\u0644\u0633\u0644\u0629 \u0642\u0648\u0649 \u0647\u0648 \u0646\u0635\u0641 \u0642\u0637\u0631 \u0623\u0643\u0628\u0631 \u0642\u0631\u0635 \u062A\u062A\u0642\u0627\u0631\u0628 \u0641\u064A\u0647 \u0627\u0644\u0645\u062A\u0633\u0644\u0633\u0644\u0629\u060C \u0648\u0647\u0648 \u0625\u0645\u0627 \u0639\u062F\u062F \u062D\u0642\u064A\u0642\u064A \u063A\u064A\u0631 \u0633\u0627\u0644\u0628 \u0623\u0648 \u221E. \u0648\u0641\u0642\u064B\u0627 \u0644\u0645\u0628\u0631\u0647\u0646\u0629 \u0643\u0648\u0634\u064A-\u0647\u0627\u062F\u0627\u0645\u0627\u0631\u060C \u062A\u0639\u0637\u0649 \u0646\u0635\u0641 \u0642\u0637\u0631 \u062A\u0642\u0627\u0631\u0628 \u0645\u062A\u0633\u0644\u0633\u0644\u0629 \u0645\u0646 \u0627\u0644\u0634\u0643\u0644 \u060C \u0645\u0639 \u060C \u0628\u0648\u0627\u0633\u0637\u0629 \u0627\u0644\u0639\u0628\u0627\u0631\u0629 \u0627\u0644\u062A\u0627\u0644\u064A\u0629: \u0625\u0630\u0627 \u0643\u0627\u0646 \u0646\u0635\u0641 \u0642\u0637\u0631 \u062A\u0642\u0627\u0631\u0628 \u0645\u062A\u0633\u0644\u0633\u0644\u0629 \u062F\u0627\u0644\u0629 \u0647\u0648 \u0645\u0627 \u0644\u0627 \u0646\u0647\u0627\u064A\u0629\u060C \u064A\u0645\u0643\u0646 \u0623\u0646 \u062A\u0645\u062F\u062F \u0627\u0644\u062F\u0627\u0644\u0629 \u0625\u0644\u0649 \u062F\u0627\u0644\u0629 \u0643\u0627\u0645\u0644\u0629."@ar . "16363"^^ . "Konvergensradien f\u00F6r en potensserie \u00E4r radien f\u00F6r den st\u00F6rsta cirkelskiva f\u00F6r vilken serien \u00E4r konvergent. Den \u00E4r endera ett icke-negativt reellt tal eller \u221E. N\u00E4r radien \u00E4r positiv \u00E4r potensserien absolutkonvergent innanf\u00F6r den \u00F6ppna cirkelskivan best\u00E4md av konvergensradien och divergent utanf\u00F6r denna radie."@sv . . . . . . . . . . "\u53CE\u675F\u534A\u5F84"@ja . "In mathematics, the radius of convergence of a power series is the radius of the largest disk at the center of the series in which the series converges. It is either a non-negative real number or . When it is positive, the power series converges absolutely and uniformly on compact sets inside the open disk of radius equal to the radius of convergence, and it is the Taylor series of the analytic function to which it converges. In case of multiple singularities of a function (singularities are those values of the argument for which the function is not defined), the radius of convergence is the shortest or minimum of all the respective distances (which are all non-negative numbers) calculated from the center of the disk of convergence to the respective singularities of the function."@en . . "Radi de converg\u00E8ncia"@ca . . "Konvergensradien f\u00F6r en potensserie \u00E4r radien f\u00F6r den st\u00F6rsta cirkelskiva f\u00F6r vilken serien \u00E4r konvergent. Den \u00E4r endera ett icke-negativt reellt tal eller \u221E. N\u00E4r radien \u00E4r positiv \u00E4r potensserien absolutkonvergent innanf\u00F6r den \u00F6ppna cirkelskivan best\u00E4md av konvergensradien och divergent utanf\u00F6r denna radie."@sv . "\u53CE\u675F\u534A\u5F84(\u3057\u3085\u3046\u305D\u304F\u306F\u3093\u3051\u3044\u3001radius of convergence) \u3068\u306F\u3001\u51AA\u7D1A\u6570\u304C\u53CE\u675F\u3059\u308B\u5B9A\u7FA9\u57DF\u3092\u4E0E\u3048\u308B\u975E\u8CA0\u91CF\uFF08\u5B9F\u6570\u3042\u308B\u3044\u306F\u221E\uFF09\u3067\u3042\u308B\u3002 \u6B21\u306E\u51AA\u7D1A\u6570\u3092\u8003\u3048\u308B\u3002 \u305F\u3060\u3057\u3001\u4E2D\u5FC3 a \u3084\u4FC2\u6570 cn \u306F\u8907\u7D20\u6570\uFF08\u7279\u306B\u5B9F\u6570\uFF09\u3068\u3059\u308B\u3002\u6B21\u306E\u6761\u4EF6\u304C\u6210\u7ACB\u3059\u308B\u3068\u304D\u3001 r \u3092\u3053\u306E\u7D1A\u6570\u306E\u53CE\u675F\u534A\u5F84\u3068\u3044\u3046\u3002 \u3067\u3042\u308B\u3068\u304D\u3001\u7D1A\u6570\u306F\u53CE\u675F\u3057\u3001 \u3067\u3042\u308B\u3068\u304D\u3001\u7D1A\u6570\u306F\u767A\u6563\u3059\u308B\u3002 \u3082\u3057\u3001\u7D1A\u6570\u304C\u5168\u3066\u306E\u8907\u7D20\u6570 z \u306B\u95A2\u3057\u3066\u53CE\u675F\u3059\u308B\u306A\u3089\u3070\u3001\u53CE\u675F\u534A\u5F84\u306F \u221E \u3068\u306A\u308B\u3002"@ja . . "En matem\u00E1ticas, seg\u00FAn el teorema de Cauchy-Hadamard, el radio de convergencia de una serie de la forma , con , viene dado por la expresi\u00F3n:"@es . . . "\u041A\u0440\u0443\u0433 \u0441\u0445\u043E\u0434\u0438\u043C\u043E\u0441\u0442\u0438 \u0441\u0442\u0435\u043F\u0435\u043D\u043D\u043E\u0433\u043E \u0440\u044F\u0434\u0430 \u2014 \u044D\u0442\u043E \u043A\u0440\u0443\u0433 \u0432\u0438\u0434\u0430 , , \u0432 \u043A\u043E\u0442\u043E\u0440\u043E\u043C \u0440\u044F\u0434 \u0430\u0431\u0441\u043E\u043B\u044E\u0442\u043D\u043E \u0441\u0445\u043E\u0434\u0438\u0442\u0441\u044F, \u0430 \u0432\u043D\u0435 \u0435\u0433\u043E, \u043F\u0440\u0438 , \u0440\u0430\u0441\u0445\u043E\u0434\u0438\u0442\u0441\u044F. \u0418\u043D\u044B\u043C\u0438 \u0441\u043B\u043E\u0432\u0430\u043C\u0438, \u043A\u0440\u0443\u0433 \u0441\u0445\u043E\u0434\u0438\u043C\u043E\u0441\u0442\u0438 \u0441\u0442\u0435\u043F\u0435\u043D\u043D\u043E\u0433\u043E \u0440\u044F\u0434\u0430 \u0435\u0441\u0442\u044C \u0432\u043D\u0443\u0442\u0440\u0435\u043D\u043D\u043E\u0441\u0442\u044C \u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432\u0430 \u0442\u043E\u0447\u0435\u043A \u0441\u0445\u043E\u0434\u0438\u043C\u043E\u0441\u0442\u0438 \u0440\u044F\u0434\u0430. \u041A\u0440\u0443\u0433 \u0441\u0445\u043E\u0434\u0438\u043C\u043E\u0441\u0442\u0438 \u043C\u043E\u0436\u0435\u0442 \u0432\u044B\u0440\u043E\u0436\u0434\u0430\u0442\u044C\u0441\u044F \u0432 \u043F\u0443\u0441\u0442\u043E\u0435 \u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432\u043E, \u043A\u043E\u0433\u0434\u0430 , \u0438 \u043C\u043E\u0436\u0435\u0442 \u0441\u043E\u0432\u043F\u0430\u0434\u0430\u0442\u044C \u0441\u043E \u0432\u0441\u0435\u0439 \u043F\u043B\u043E\u0441\u043A\u043E\u0441\u0442\u044C\u044E \u043F\u0435\u0440\u0435\u043C\u0435\u043D\u043D\u043E\u0433\u043E , \u043A\u043E\u0433\u0434\u0430 ."@ru . . "In analisi matematica, il raggio di convergenza \u00E8 un numero non negativo (non necessariamente finito) associato a una serie di potenze a coefficienti reali o complessi che, intuitivamente, informa sul comportamento globale della serie in materia di convergenza. Pi\u00F9 in dettaglio, il raggio di convergenza misura l'estensione dell'insieme aperto pi\u00F9 grande su cui la serie converge."@it . "Konvergensradie"@sv . . . . . "Radius of convergence"@en . . . . . "\u0646\u0635\u0641 \u0642\u0637\u0631 \u0627\u0644\u062A\u0642\u0627\u0631\u0628"@ar . . . "\u0423 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0447\u043D\u043E\u043C\u0443 \u0430\u043D\u0430\u043B\u0456\u0437\u0456 (\u043A\u043E\u043C\u043F\u043B\u0435\u043A\u0441\u043D\u043E\u043C\u0443 \u0430\u0431\u043E \u0434\u0456\u0439\u0441\u043D\u043E\u043C\u0443) \u0440\u0430\u0434\u0456\u0443\u0441\u043E\u043C \u0437\u0431\u0456\u0436\u043D\u043E\u0441\u0442\u0456 \u0441\u0442\u0435\u043F\u0435\u043D\u0435\u0432\u043E\u0433\u043E \u0440\u044F\u0434\u0443 \u043D\u0430\u0437\u0438\u0432\u0430\u0454\u0442\u044C\u0441\u044F \u043D\u0435\u0432\u0456\u0434'\u0454\u043C\u043D\u0435 \u0434\u0456\u0439\u0441\u043D\u0435 \u0447\u0438\u0441\u043B\u043E (\u0430\u0431\u043E \u043D\u0435\u0441\u043A\u0456\u043D\u0447\u0435\u043D\u043D\u0456\u0441\u0442\u044C), \u0442\u0430\u043A\u0435 \u0449\u043E \u0432 \u0443\u0441\u0456\u0445 \u0442\u043E\u0447\u043A\u0430\u0445 \u0440\u043E\u0437\u0442\u0430\u0448\u043E\u0432\u0430\u043D\u0438\u0445 \u043D\u0430 \u0432\u0456\u0434\u0441\u0442\u0430\u043D\u0456 \u0432\u0456\u0434 \u0446\u0435\u043D\u0442\u0440\u0443 \u0441\u0442\u0435\u043F\u0435\u043D\u0435\u0432\u043E\u0433\u043E \u0440\u044F\u0434\u0443 \u043C\u0435\u043D\u0448\u0456\u0439, \u043D\u0456\u0436 \u0446\u0435 \u0447\u0438\u0441\u043B\u043E \u0446\u0435\u0439 \u0440\u044F\u0434 \u0437\u0431\u0456\u0433\u0430\u0454\u0442\u044C\u0441\u044F. \u0414\u043E \u0442\u043E\u0433\u043E \u0436 \u0432\u0438\u044F\u0432\u043B\u044F\u0454\u0442\u044C\u0441\u044F, \u0449\u043E \u0440\u044F\u0434 \u0437\u0431\u0456\u0433\u0430\u0454\u0442\u044C\u0441\u044F \u0430\u0431\u0441\u043E\u043B\u044E\u0442\u043D\u043E \u0443 \u0432\u0441\u0456\u0445 \u0442\u043E\u0447\u043A\u0430\u0445 \u043A\u0440\u0443\u0433\u0430 \u0437 \u0446\u0438\u043C \u0440\u0430\u0434\u0456\u0443\u0441\u043E\u043C \u0456 \u0432 \u0443\u0441\u0456\u0445 \u0442\u043E\u0447\u043A\u0430\u0445 \u0440\u043E\u0437\u0442\u0430\u0448\u043E\u0432\u0430\u043D\u0438\u0445 \u043D\u0430 \u0432\u0456\u0434\u0441\u0442\u0430\u043D\u0456 \u0432\u0456\u0434 \u0446\u0435\u043D\u0442\u0440\u0443 \u0441\u0442\u0435\u043F\u0435\u043D\u0435\u0432\u043E\u0433\u043E \u0440\u044F\u0434\u0443 \u0431\u0456\u043B\u044C\u0448\u0456\u0439, \u043D\u0456\u0436 \u0440\u0430\u0434\u0456\u0443\u0441 \u0437\u0431\u0456\u0436\u043D\u043E\u0441\u0442\u0456, \u0440\u044F\u0434 \u043E\u0431\u043E\u0432'\u044F\u0437\u043A\u043E\u0432\u043E \u0440\u043E\u0437\u0431\u0456\u0433\u0430\u0454\u0442\u044C\u0441\u044F. \u041F\u043E\u043D\u044F\u0442\u0442\u044F \u0441\u0442\u0435\u043F\u0435\u043D\u0435\u0432\u0438\u0445 \u0440\u044F\u0434\u0456\u0432 \u0457\u0445 \u0440\u0430\u0434\u0456\u0443\u0441\u0456\u0432 \u0456 \u043A\u0440\u0443\u0433\u0456\u0432 \u0437\u0431\u0456\u0436\u043D\u043E\u0441\u0442\u0456 \u0432\u0456\u0434\u0456\u0433\u0440\u0430\u044E\u0442\u044C \u0434\u0443\u0436\u0435 \u0432\u0430\u0436\u043B\u0438\u0432\u0443 \u0440\u043E\u043B\u044C \u0432 \u0440\u0456\u0437\u043D\u0438\u0445 \u0440\u043E\u0437\u0434\u0456\u043B\u0430\u0445 \u0430\u043D\u0430\u043B\u0456\u0437\u0443."@uk . . "Rayon de convergence"@fr . "Der Konvergenzradius ist in der Analysis eine Eigenschaft einer Potenzreihe der Form , die angibt, in welchem Bereich der reellen Gerade oder der komplexen Ebene f\u00FCr die Potenzreihe Konvergenz garantiert ist."@de . . "61476"^^ . . . "\u0420\u0430\u0434\u0456\u0443\u0441 \u0437\u0431\u0456\u0436\u043D\u043E\u0441\u0442\u0456"@uk . . "1117893272"^^ . . . "Raio de converg\u00EAncia"@pt . . . . . "In analisi matematica, il raggio di convergenza \u00E8 un numero non negativo (non necessariamente finito) associato a una serie di potenze a coefficienti reali o complessi che, intuitivamente, informa sul comportamento globale della serie in materia di convergenza. Pi\u00F9 in dettaglio, il raggio di convergenza misura l'estensione dell'insieme aperto pi\u00F9 grande su cui la serie converge."@it . "Na teoria das S\u00E9ries de Taylor, o raio de converg\u00EAncia pode ser zero, um n\u00FAmero positivo ou ainda infinito. Indica o raio da circunfer\u00EAncia em torno do centro da s\u00E9rie de Taylor dentro da qual a s\u00E9rie converge. No caso das s\u00E9ries reais, pode-se garantir a converg\u00EAncia no intervalo aberto , onde \u00E9 centro da s\u00E9rie e \u00E9 o raio de converg\u00EAncia. Nada se pode afirmar sobre a converg\u00EAncia nos extremos do intervalo.eNo caso das s\u00E9ries complexas, pode-se garantir que a s\u00E9rie convirja na bola aberta . Mais uma vez, nada se pode afirmar sobre a circunfer\u00EAncia A f\u00F3rmula de Hadamard permite obter o valor do raio de converg\u00EAncia: , onde s\u00E3o os coeficientes da s\u00E9rie: Existe um forma alternativa que \u00E9:, quando este limite existe."@pt . "\u6536\u655B\u534A\u5F84\u662F\u6570\u5B66\u5206\u6790\u4E2D\u4E0E\u5E42\u7EA7\u6570\u6709\u5173\u7684\u6982\u5FF5\u3002\u4E00\u4E2A\u5E42\u7EA7\u6570\u7684\u6536\u655B\u534A\u5F84\u662F\u4E00\u4E2A\u975E\u8D1F\u7684\u6269\u5C55\u5B9E\u6570\uFF08\u5305\u62EC\u65E0\u7A77\u5927\uFF09\u3002\u6536\u655B\u534A\u5F84\u8868\u793A\u5E42\u7EA7\u6570\u6536\u655B\u7684\u8303\u56F4\u3002\u5728\u6536\u655B\u534A\u5F84\u5185\u7684\u7D27\u96C6\u4E0A\uFF0C\u5E42\u7EA7\u6570\u5BF9\u5E94\u7684\u51FD\u6570\u4E00\u81F4\u6536\u655B\uFF0C\u5E76\u4E14\u5E42\u7EA7\u6570\u5C31\u662F\u6B64\u51FD\u6570\u5C55\u5F00\u5F97\u5230\u7684\u6CF0\u52D2\u7EA7\u6570\u3002\u4F46\u662F\uFF0C\u5728\u6536\u655B\u534A\u5F84\u4E0A\u5E42\u7EA7\u6570\u7684\u655B\u6563\u6027\u662F\u4E0D\u786E\u5B9A\u7684\u3002"@zh . . . . "En matem\u00E0tiques, el radi de converg\u00E8ncia d'una s\u00E8rie de pot\u00E8ncies enteres segons el teorema de Cauchy-Hadamard ve donat per l'expressi\u00F3:"@ca . . . . . . . "Polom\u011Br konvergence"@cs . . . . . . . "\u0423 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0447\u043D\u043E\u043C\u0443 \u0430\u043D\u0430\u043B\u0456\u0437\u0456 (\u043A\u043E\u043C\u043F\u043B\u0435\u043A\u0441\u043D\u043E\u043C\u0443 \u0430\u0431\u043E \u0434\u0456\u0439\u0441\u043D\u043E\u043C\u0443) \u0440\u0430\u0434\u0456\u0443\u0441\u043E\u043C \u0437\u0431\u0456\u0436\u043D\u043E\u0441\u0442\u0456 \u0441\u0442\u0435\u043F\u0435\u043D\u0435\u0432\u043E\u0433\u043E \u0440\u044F\u0434\u0443 \u043D\u0430\u0437\u0438\u0432\u0430\u0454\u0442\u044C\u0441\u044F \u043D\u0435\u0432\u0456\u0434'\u0454\u043C\u043D\u0435 \u0434\u0456\u0439\u0441\u043D\u0435 \u0447\u0438\u0441\u043B\u043E (\u0430\u0431\u043E \u043D\u0435\u0441\u043A\u0456\u043D\u0447\u0435\u043D\u043D\u0456\u0441\u0442\u044C), \u0442\u0430\u043A\u0435 \u0449\u043E \u0432 \u0443\u0441\u0456\u0445 \u0442\u043E\u0447\u043A\u0430\u0445 \u0440\u043E\u0437\u0442\u0430\u0448\u043E\u0432\u0430\u043D\u0438\u0445 \u043D\u0430 \u0432\u0456\u0434\u0441\u0442\u0430\u043D\u0456 \u0432\u0456\u0434 \u0446\u0435\u043D\u0442\u0440\u0443 \u0441\u0442\u0435\u043F\u0435\u043D\u0435\u0432\u043E\u0433\u043E \u0440\u044F\u0434\u0443 \u043C\u0435\u043D\u0448\u0456\u0439, \u043D\u0456\u0436 \u0446\u0435 \u0447\u0438\u0441\u043B\u043E \u0446\u0435\u0439 \u0440\u044F\u0434 \u0437\u0431\u0456\u0433\u0430\u0454\u0442\u044C\u0441\u044F. \u0414\u043E \u0442\u043E\u0433\u043E \u0436 \u0432\u0438\u044F\u0432\u043B\u044F\u0454\u0442\u044C\u0441\u044F, \u0449\u043E \u0440\u044F\u0434 \u0437\u0431\u0456\u0433\u0430\u0454\u0442\u044C\u0441\u044F \u0430\u0431\u0441\u043E\u043B\u044E\u0442\u043D\u043E \u0443 \u0432\u0441\u0456\u0445 \u0442\u043E\u0447\u043A\u0430\u0445 \u043A\u0440\u0443\u0433\u0430 \u0437 \u0446\u0438\u043C \u0440\u0430\u0434\u0456\u0443\u0441\u043E\u043C \u0456 \u0432 \u0443\u0441\u0456\u0445 \u0442\u043E\u0447\u043A\u0430\u0445 \u0440\u043E\u0437\u0442\u0430\u0448\u043E\u0432\u0430\u043D\u0438\u0445 \u043D\u0430 \u0432\u0456\u0434\u0441\u0442\u0430\u043D\u0456 \u0432\u0456\u0434 \u0446\u0435\u043D\u0442\u0440\u0443 \u0441\u0442\u0435\u043F\u0435\u043D\u0435\u0432\u043E\u0433\u043E \u0440\u044F\u0434\u0443 \u0431\u0456\u043B\u044C\u0448\u0456\u0439, \u043D\u0456\u0436 \u0440\u0430\u0434\u0456\u0443\u0441 \u0437\u0431\u0456\u0436\u043D\u043E\u0441\u0442\u0456, \u0440\u044F\u0434 \u043E\u0431\u043E\u0432'\u044F\u0437\u043A\u043E\u0432\u043E \u0440\u043E\u0437\u0431\u0456\u0433\u0430\u0454\u0442\u044C\u0441\u044F. \u041F\u043E\u043D\u044F\u0442\u0442\u044F \u0441\u0442\u0435\u043F\u0435\u043D\u0435\u0432\u0438\u0445 \u0440\u044F\u0434\u0456\u0432 \u0457\u0445 \u0440\u0430\u0434\u0456\u0443\u0441\u0456\u0432 \u0456 \u043A\u0440\u0443\u0433\u0456\u0432 \u0437\u0431\u0456\u0436\u043D\u043E\u0441\u0442\u0456 \u0432\u0456\u0434\u0456\u0433\u0440\u0430\u044E\u0442\u044C \u0434\u0443\u0436\u0435 \u0432\u0430\u0436\u043B\u0438\u0432\u0443 \u0440\u043E\u043B\u044C \u0432 \u0440\u0456\u0437\u043D\u0438\u0445 \u0440\u043E\u0437\u0434\u0456\u043B\u0430\u0445 \u0430\u043D\u0430\u043B\u0456\u0437\u0443."@uk . "En matem\u00E0tiques, el radi de converg\u00E8ncia d'una s\u00E8rie de pot\u00E8ncies enteres segons el teorema de Cauchy-Hadamard ve donat per l'expressi\u00F3:"@ca . . . "Na teoria das S\u00E9ries de Taylor, o raio de converg\u00EAncia pode ser zero, um n\u00FAmero positivo ou ainda infinito. Indica o raio da circunfer\u00EAncia em torno do centro da s\u00E9rie de Taylor dentro da qual a s\u00E9rie converge. No caso das s\u00E9ries reais, pode-se garantir a converg\u00EAncia no intervalo aberto , onde \u00E9 centro da s\u00E9rie e \u00E9 o raio de converg\u00EAncia. Nada se pode afirmar sobre a converg\u00EAncia nos extremos do intervalo.eNo caso das s\u00E9ries complexas, pode-se garantir que a s\u00E9rie convirja na bola aberta . Mais uma vez, nada se pode afirmar sobre a circunfer\u00EAncia , onde s\u00E3o os coeficientes da s\u00E9rie:"@pt . .