"\u9670\u8A08\u7B97"@ja . . "Em matem\u00E1tica, costumava-se utilizar o termo c\u00E1lculo umbral em refer\u00EAncia a surpreendentes similaridades entre equa\u00E7\u00F5es polinomiais e certas t\u00E9cnicas emp\u00EDricas utilizadas para 'demonstr\u00E1-las'. Tais t\u00E9cnicas foram apresentadas por John Blissard em 1861, sendo por vezes chamadas de m\u00E9todo simb\u00F3lico de Blissard. S\u00E3o eventualmente atribu\u00EDdas a \u00C9douard Lucas ou James Joseph Sylvester, que usaram estas t\u00E9cnicas extensivamente. Nas d\u00E9cadas de 1930 e 1940, Eric Temple Bell esfor\u00E7ou-se por estabelecer uma justificativa matem\u00E1tica rigorosa para o c\u00E1lculo umbral, sem lograr \u00EAxito completo. Na d\u00E9cada de 1970, Steven Roman, Gian-Carlo Rota e outros matem\u00E1ticos desenvolveram um arcabou\u00E7o te\u00F3rico para o justificar o c\u00E1lculo umbral atrav\u00E9s de formas lineares em espa\u00E7os de polin\u00F4mios. Atualmente, por c\u00E1lculo umbral entende-se principalmente o m\u00E9todo de estudo de , a\u00ED inclu\u00EDdas as sequ\u00EAncias polinomiais do , assim como ."@pt . . "Der Umbral-Kalk\u00FCl oder umbrale Kalk\u00FCl (engl. umbral calculus, ferner lat. umbra, \u201Eder Schatten\u201C) ist ein Teilbereich der Kombinatorik, der aus der Beobachtung der formalen \u00C4hnlichkeit bei der Ableitung polynomialer Identit\u00E4ten entstand, bei denen Indizes wie Exponenten behandelt wurden. Da man daf\u00FCr lange keine Erkl\u00E4rung fand, wurde die Bezeichnung Schatten-Kalk\u00FCl (Umbral-Kalk\u00FCl) benutzt. Die Techniken gehen bis in das 19. Jahrhundert zur\u00FCck, insbesondere auf John Blissard (1861), nach dem von Blissards symbolischer Methode gesprochen wurde, sie wurden aber auch unter anderem von \u00C9douard Lucas (der sie symbolische Methode nannte) und James Joseph Sylvester benutzt. Von Sylvester stammt auch die Benennung umbral. Eric Temple Bell versuchte in den 1930er Jahren den Methoden (mit wenig Erfolg bei der Durchsetzung) eine strenge Grundlage zu geben, das gelang erst Gian-Carlo Rota und Steven Roman in den 1970er Jahren. Sie wurden aber zuvor schon zum Beispiel von John Riordan in der Kombinatorik weiter verwendet."@de . . "C\u00E1lculo umbral"@pt . . . . . . . "1088549876"^^ . "\u0422\u0435\u043D\u0435\u0432\u043E\u0435 \u0438\u0441\u0447\u0438\u0441\u043B\u0435\u043D\u0438\u0435"@ru . . . . "Calcul ombral"@fr . "In matematica, prima degli anni 1970, con il termine calcolo umbrale si indicavano le sorprendenti somiglianze tra molte equazioni polinomiali allora prive di collegamenti logici, nonch\u00E9 certe tecniche poco giustificate che potevano essere usate per 'dimostrare' tali equazioni. Queste tecniche erano state introdotte nel XIX secolo e da taluni sono state chiamate metodo simbolico di Blissard, da altri sono state attribuite a James Joseph Sylvester (che le ha utilizzate ampiamente) e da altri ancora a \u00C9douard Lucas."@it . . . "En matem\u00E1ticas, antes de la d\u00E9cada de 1970, el t\u00E9rmino c\u00E1lculo umbral se refer\u00EDa a la sorprendente similitud entre las ecuaciones algebraicas y las exponenciales en la aplicaci\u00F3n de ciertas t\u00E9cnicas no estrictamente rigurosas utilizadas para \"probarlas\", aparentemente no relacionadas entre s\u00ED. Aqu\u00ED, la ra\u00EDz latina umbral se utilizaba con el significado de sombra, haciendo referencia a la relaci\u00F3n entre super\u00EDndices exponenciales y su sombra, los sub\u00EDndices que se relacionan con ellos."@es . . "Der Umbral-Kalk\u00FCl oder umbrale Kalk\u00FCl (engl. umbral calculus, ferner lat. umbra, \u201Eder Schatten\u201C) ist ein Teilbereich der Kombinatorik, der aus der Beobachtung der formalen \u00C4hnlichkeit bei der Ableitung polynomialer Identit\u00E4ten entstand, bei denen Indizes wie Exponenten behandelt wurden. Da man daf\u00FCr lange keine Erkl\u00E4rung fand, wurde die Bezeichnung Schatten-Kalk\u00FCl (Umbral-Kalk\u00FCl) benutzt."@de . . . . . "En matem\u00E1ticas, antes de la d\u00E9cada de 1970, el t\u00E9rmino c\u00E1lculo umbral se refer\u00EDa a la sorprendente similitud entre las ecuaciones algebraicas y las exponenciales en la aplicaci\u00F3n de ciertas t\u00E9cnicas no estrictamente rigurosas utilizadas para \"probarlas\", aparentemente no relacionadas entre s\u00ED. Aqu\u00ED, la ra\u00EDz latina umbral se utilizaba con el significado de sombra, haciendo referencia a la relaci\u00F3n entre super\u00EDndices exponenciales y su sombra, los sub\u00EDndices que se relacionan con ellos. Estas t\u00E9cnicas fueron introducidas por y a veces se denominan \"m\u00E9todo simb\u00F3lico de Blissard\". A menudo tambi\u00E9n se atribuyen a \u00C9douard Lucas (o a James Joseph Sylvester), que usaron la t\u00E9cnica extensivamente.\u200B"@es . . "Umbral calculus"@en . "\u0422\u0435\u043D\u0435\u0432\u043E\u0435 \u0438\u0441\u0447\u0438\u0441\u043B\u0435\u043D\u0438\u0435 (\u043E\u0442 \u0430\u043D\u0433\u043B. Umbral calculus, \u0434\u0430\u043B\u0435\u0435 \u043E\u0442 \u043B\u0430\u0442. umbra \u2014 \u00AB\u0442\u0435\u043D\u044C\u00BB) \u2014 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0447\u0435\u0441\u043A\u0438\u0439 \u043C\u0435\u0442\u043E\u0434 \u043F\u043E\u043B\u0443\u0447\u0435\u043D\u0438\u044F \u043D\u0435\u043A\u043E\u0442\u043E\u0440\u044B\u0445 \u0430\u043B\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043A\u0438\u0445 \u0442\u043E\u0436\u0434\u0435\u0441\u0442\u0432. \u0414\u043E 1970-\u0445 \u0442\u0435\u0440\u043C\u0438\u043D \u043E\u0442\u043D\u043E\u0441\u0438\u043B\u0441\u044F \u043A \u0441\u0445\u043E\u0436\u0435\u0441\u0442\u0438 \u043D\u0435\u043A\u043E\u0442\u043E\u0440\u044B\u0445 \u0432\u043D\u0435\u0448\u043D\u0435 \u043D\u0435\u0441\u0432\u044F\u0437\u0430\u043D\u043D\u044B\u0445 \u0430\u043B\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043A\u0438\u0445 \u0442\u043E\u0436\u0434\u0435\u0441\u0442\u0432, \u0430 \u0442\u0430\u043A\u0436\u0435 \u043A \u0442\u0435\u0445\u043D\u0438\u043A\u0430\u043C, \u0438\u0441\u043F\u043E\u043B\u044C\u0437\u043E\u0432\u0430\u043D\u043D\u044B\u0445 \u0434\u043B\u044F \u0434\u043E\u043A\u0430\u0437\u0430\u0442\u0435\u043B\u044C\u0441\u0442\u0432\u0430 \u044D\u0442\u0438\u0445 \u0442\u043E\u0436\u0434\u0435\u0441\u0442\u0432. \u042D\u0442\u0438 \u0442\u0435\u0445\u043D\u0438\u043A\u0438 \u043F\u0440\u0435\u0434\u043B\u043E\u0436\u0438\u043B \u0414\u0436\u043E\u043D \u0411\u043B\u0438\u0441\u0441\u0430\u0440\u0434 \u0438 \u043E\u043D\u0438 \u0438\u043D\u043E\u0433\u0434\u0430 \u043D\u0430\u0437\u044B\u0432\u0430\u044E\u0442\u0441\u044F \u0441\u0438\u043C\u0432\u043E\u043B\u0438\u0447\u0435\u0441\u043A\u0438\u043C \u043C\u0435\u0442\u043E\u0434\u043E\u043C \u0411\u043B\u0438\u0441\u0441\u0430\u0440\u0434\u0430. \u0418\u0445 \u0447\u0430\u0441\u0442\u043E \u043F\u0440\u0438\u043F\u0438\u0441\u044B\u0432\u0430\u044E\u0442 \u042D\u0434\u0443\u0430\u0440\u0434\u0443 \u041B\u044E\u043A\u0430 (\u0438\u043B\u0438 \u0414\u0436\u0435\u0439\u043C\u0441\u0443 \u0414\u0436\u043E\u0437\u0435\u0444\u0443 \u0421\u0438\u043B\u044C\u0432\u0435\u0441\u0442\u0440\u0443), \u043A\u043E\u0442\u043E\u0440\u044B\u0435 \u0438\u0445 \u0438\u043D\u0442\u0435\u043D\u0441\u0438\u0432\u043D\u043E \u0438\u0441\u043F\u043E\u043B\u044C\u0437\u043E\u0432\u0430\u043B\u0438. \u0412 1930-\u0445 \u0438 1940-\u0445 \u042D\u0440\u0438\u043A \u0422\u0435\u043C\u043F\u043B \u0411\u0435\u043B\u043B \u043F\u044B\u0442\u0430\u043B\u0441\u044F \u043F\u043E\u0441\u0442\u0430\u0432\u0438\u0442\u044C \u0442\u0435\u043D\u0435\u0432\u043E\u0435 \u0438\u0441\u0447\u0438\u0441\u043B\u0435\u043D\u0438\u0435 \u043D\u0430 \u0441\u0442\u0440\u043E\u0433\u043E\u0435 \u043E\u0441\u043D\u043E\u0432\u0430\u043D\u0438\u0435."@ru . . . . . . . . . . . "Termin rachunek umbralny by\u0142 pierwotnie zwi\u0105zany z zaskakuj\u0105cymi podobie\u0144stwami pomi\u0119dzy pozornie niepowi\u0105zanymi r\u00F3wnaniami algebraicznymi i pewnymi niejasnymi technikami u\u017Cytymi w celu ich uzyskania (ale nie udowodnienia). Te techniki zosta\u0142y wprowadzone przez i s\u0105 czasami nazywane metod\u0105 symboliczn\u0105 Blissarda. Cz\u0119sto s\u0105 one przypisywane innym matematykom (\u00C9douard Lucas, James Joseph Sylvester), kt\u00F3rzy wykorzystywali te techniki ekstensywnie. W latach 30. i 40. XX wieku spr\u00F3bowa\u0142 stworzy\u0107 rygorystyczne podstawy rachunku umbralnego."@pl . "10249"^^ . . . . . . . "In matematica, prima degli anni 1970, con il termine calcolo umbrale si indicavano le sorprendenti somiglianze tra molte equazioni polinomiali allora prive di collegamenti logici, nonch\u00E9 certe tecniche poco giustificate che potevano essere usate per 'dimostrare' tali equazioni. Queste tecniche erano state introdotte nel XIX secolo e da taluni sono state chiamate metodo simbolico di Blissard, da altri sono state attribuite a James Joseph Sylvester (che le ha utilizzate ampiamente) e da altri ancora a \u00C9douard Lucas. Negli anni 1930 e 1940 Eric Temple Bell ha cercato di fornire il calcolo umbrale di fondamenti rigorosi, riuscendoci solo in parte. Negli anni 1970 Gian-Carlo Rota, Steven Roman e altri sono riusciti a sviluppare il calcolo umbrale sulla solida base dei funzionali lineari sugli spazi di polinomi. Attualmente il calcolo umbrale viene considerato essenzialmente uno strumento per lo studio delle sequenze di Sheffer, e in particolare delle sequenze polinomiali di tipo binomiale e delle ."@it . . . . "\u0422\u0435\u043D\u0435\u0432\u043E\u0435 \u0438\u0441\u0447\u0438\u0441\u043B\u0435\u043D\u0438\u0435 (\u043E\u0442 \u0430\u043D\u0433\u043B. Umbral calculus, \u0434\u0430\u043B\u0435\u0435 \u043E\u0442 \u043B\u0430\u0442. umbra \u2014 \u00AB\u0442\u0435\u043D\u044C\u00BB) \u2014 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0447\u0435\u0441\u043A\u0438\u0439 \u043C\u0435\u0442\u043E\u0434 \u043F\u043E\u043B\u0443\u0447\u0435\u043D\u0438\u044F \u043D\u0435\u043A\u043E\u0442\u043E\u0440\u044B\u0445 \u0430\u043B\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043A\u0438\u0445 \u0442\u043E\u0436\u0434\u0435\u0441\u0442\u0432. \u0414\u043E 1970-\u0445 \u0442\u0435\u0440\u043C\u0438\u043D \u043E\u0442\u043D\u043E\u0441\u0438\u043B\u0441\u044F \u043A \u0441\u0445\u043E\u0436\u0435\u0441\u0442\u0438 \u043D\u0435\u043A\u043E\u0442\u043E\u0440\u044B\u0445 \u0432\u043D\u0435\u0448\u043D\u0435 \u043D\u0435\u0441\u0432\u044F\u0437\u0430\u043D\u043D\u044B\u0445 \u0430\u043B\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043A\u0438\u0445 \u0442\u043E\u0436\u0434\u0435\u0441\u0442\u0432, \u0430 \u0442\u0430\u043A\u0436\u0435 \u043A \u0442\u0435\u0445\u043D\u0438\u043A\u0430\u043C, \u0438\u0441\u043F\u043E\u043B\u044C\u0437\u043E\u0432\u0430\u043D\u043D\u044B\u0445 \u0434\u043B\u044F \u0434\u043E\u043A\u0430\u0437\u0430\u0442\u0435\u043B\u044C\u0441\u0442\u0432\u0430 \u044D\u0442\u0438\u0445 \u0442\u043E\u0436\u0434\u0435\u0441\u0442\u0432. \u042D\u0442\u0438 \u0442\u0435\u0445\u043D\u0438\u043A\u0438 \u043F\u0440\u0435\u0434\u043B\u043E\u0436\u0438\u043B \u0414\u0436\u043E\u043D \u0411\u043B\u0438\u0441\u0441\u0430\u0440\u0434 \u0438 \u043E\u043D\u0438 \u0438\u043D\u043E\u0433\u0434\u0430 \u043D\u0430\u0437\u044B\u0432\u0430\u044E\u0442\u0441\u044F \u0441\u0438\u043C\u0432\u043E\u043B\u0438\u0447\u0435\u0441\u043A\u0438\u043C \u043C\u0435\u0442\u043E\u0434\u043E\u043C \u0411\u043B\u0438\u0441\u0441\u0430\u0440\u0434\u0430. \u0418\u0445 \u0447\u0430\u0441\u0442\u043E \u043F\u0440\u0438\u043F\u0438\u0441\u044B\u0432\u0430\u044E\u0442 \u042D\u0434\u0443\u0430\u0440\u0434\u0443 \u041B\u044E\u043A\u0430 (\u0438\u043B\u0438 \u0414\u0436\u0435\u0439\u043C\u0441\u0443 \u0414\u0436\u043E\u0437\u0435\u0444\u0443 \u0421\u0438\u043B\u044C\u0432\u0435\u0441\u0442\u0440\u0443), \u043A\u043E\u0442\u043E\u0440\u044B\u0435 \u0438\u0445 \u0438\u043D\u0442\u0435\u043D\u0441\u0438\u0432\u043D\u043E \u0438\u0441\u043F\u043E\u043B\u044C\u0437\u043E\u0432\u0430\u043B\u0438. \u0412 1930-\u0445 \u0438 1940-\u0445 \u042D\u0440\u0438\u043A \u0422\u0435\u043C\u043F\u043B \u0411\u0435\u043B\u043B \u043F\u044B\u0442\u0430\u043B\u0441\u044F \u043F\u043E\u0441\u0442\u0430\u0432\u0438\u0442\u044C \u0442\u0435\u043D\u0435\u0432\u043E\u0435 \u0438\u0441\u0447\u0438\u0441\u043B\u0435\u043D\u0438\u0435 \u043D\u0430 \u0441\u0442\u0440\u043E\u0433\u043E\u0435 \u043E\u0441\u043D\u043E\u0432\u0430\u043D\u0438\u0435. \u0412 1970-\u0445 \u0421\u0442\u0438\u0432\u0435\u043D \u0420\u043E\u043C\u0430\u043D, \u0438 \u0434\u0440\u0443\u0433\u0438\u0435 \u0440\u0430\u0437\u0440\u0430\u0431\u043E\u0442\u0430\u043B\u0438 \u0442\u0435\u043D\u0435\u0432\u043E\u0435 \u0438\u0441\u0447\u0438\u0441\u043B\u0435\u043D\u0438\u0435 \u0432 \u0441\u043C\u044B\u0441\u043B\u0435 \u043B\u0438\u043D\u0435\u0439\u043D\u044B\u0445 \u0444\u0443\u043D\u043A\u0446\u0438\u043E\u043D\u0430\u043B\u043E\u0432 \u043D\u0430 \u043F\u0440\u043E\u0441\u0442\u0440\u0430\u043D\u0441\u0442\u0432\u0435 \u043C\u043D\u043E\u0433\u043E\u0447\u043B\u0435\u043D\u043E\u0432. \u0412 \u043D\u0430\u0441\u0442\u043E\u044F\u0449\u0435\u0435 \u0432\u0440\u0435\u043C\u044F \u0442\u0435\u043D\u0435\u0432\u043E\u0435 \u0438\u0441\u0447\u0438\u0441\u043B\u0435\u043D\u0438\u0435 \u043E\u0442\u043D\u043E\u0441\u0438\u0442\u0441\u044F \u043A \u0438\u0437\u0443\u0447\u0435\u043D\u0438\u044E , \u0432\u043A\u043B\u044E\u0447\u0430\u044F \u043F\u043E\u0441\u043B\u0435\u0434\u043E\u0432\u0430\u0442\u0435\u043B\u044C\u043D\u043E\u0441\u0442\u0438 \u043C\u043D\u043E\u0433\u043E\u0447\u043B\u0435\u043D\u043E\u0432 \u0438 \u043F\u043E\u0441\u043B\u0435\u0434\u043E\u0432\u0430\u0442\u0435\u043B\u044C\u043D\u043E\u0441\u0442\u0438 \u0410\u043F\u043F\u0435\u043B\u044F, \u043D\u043E \u043C\u043E\u0436\u0435\u0442 \u0432\u043A\u043B\u044E\u0447\u0430\u0442\u044C \u0442\u0435\u0445\u043D\u0438\u043A\u0438 \u0438\u0441\u0447\u0438\u0441\u043B\u0435\u043D\u0438\u044F \u043A\u043E\u043D\u0435\u0447\u043D\u044B\u0445 \u0440\u0430\u0437\u043D\u043E\u0441\u0442\u0435\u0439."@ru . . "UmbralCalculus"@en . . . . "S."@en . . "Umbral_calculus&oldid=36881"@en . "Calcolo umbrale"@it . "\uC870\uD569\uB860\uC5D0\uC11C \uC74C\uACC4\uC0B0\uBC95(\u9670\u8A08\u7B97\u6CD5, \uC601\uC5B4: umbral calculus)\uC740 \uD2B9\uC815 \uC218\uC5F4 \u00B7 \uB2E4\uD56D\uC2DD\uC5F4\uC5D0\uC11C\uC758 \uC544\uB7AB\uCCA8\uC790\uB97C \uB9C8\uCE58 \uAC70\uB4ED\uC81C\uACF1\uCC98\uB7FC \uC5EC\uACA8 \uACC4\uC0B0\uD558\uB294 \uACC4\uC0B0\uBC95\uC774\uB2E4."@ko . . "In mathematics before the 1970s, the term umbral calculus referred to the surprising similarity between seemingly unrelated polynomial equations and certain \"shadowy\" techniques used to \"prove\" them. These techniques were introduced by John Blissard and are sometimes called Blissard's symbolic method. They are often attributed to \u00C9douard Lucas (or James Joseph Sylvester), who used the technique extensively."@en . "1970\u5E74\u4EE3\u4EE5\u524D\u306E\u6570\u5B66\u306B\u304A\u3044\u3066 \"umbral calculus\"\uFF08\u9670\u5F71\u306E\u7B97\u6CD5\u3001\u9670\u8A08\u7B97\uFF08\u3044\u3093\u3051\u3044\u3055\u3093\uFF09\uFF09\u306F\u3001\u3042\u308B\u7A2E\u306E\u300C\u8A3C\u660E\u300D\u306B\u7528\u3044\u3089\u308C\u308B\u3042\u308B\u7A2E\u306E\u6697\u55A9\u7684\u624B\u6CD5\u3068\u3001\u305D\u308C\u3068\u306F\u4E00\u898B\u3057\u3066\u7121\u95A2\u4FC2\u306E\u306F\u305A\u306E\u591A\u9805\u5F0F\u65B9\u7A0B\u5F0F\u3068\u306E\u9593\u306B\u6A2A\u305F\u308F\u308B\u9A5A\u304F\u3079\u304D\u95A2\u4FC2\u306B\u3064\u3044\u3066\u3044\u3046\u3082\u306E\u3067\u3042\u3063\u305F\u3002\u3053\u308C\u3089\u306E\u624B\u6CD5\u306F \u3067\u5C0E\u5165\u3055\u308C\u305F\u3082\u306E\u3067\u3001\u30D6\u30EA\u30B5\u30FC\u30C9\u306E\u8A18\u53F7\u6CD5 (Blissard's symbolic method) \u3068\u547C\u3070\u308C\u308B\u3053\u3068\u3082\u3042\u308B\u3002\u7406\u8AD6\u306E\u5C55\u958B\u306B\u306F\u3001\u3053\u306E\u624B\u6CD5\u3092\u5E83\u304F\u7528\u3044\u305F\u30EA\u30E5\u30AB\uFF08\u3084\u30B7\u30EB\u30F4\u30A7\u30B9\u30BF\u30FC\uFF09\u306E\u8CA2\u732E\u3082\u3042\u308B\u3002 1930-40\u5E74\u4EE3\u306B\u306F umbral calculus \u306B\u53B3\u683C\u306A\u8DB3\u5834\u3092\u7BC9\u304F\u3053\u3068\u3092\u8A66\u307F\u305F\u3002 1970\u5E74\u4EE3\u306B\u3001\u3001\u30B8\u30E3\u30F3\u30FB\u30AB\u30EB\u30ED\u30FB\u30ED\u30BF\u3089\u306F\u3001\u591A\u9805\u5F0F\u304B\u3089\u306A\u308B\u7A7A\u9593\u4E0A\u306E\u7DDA\u578B\u6C4E\u51FD\u6570\u3092\u7528\u3044\u3066 umbral calculus \u3092\u5C55\u958B\u3057\u305F\u3002\u73FE\u5728\u306B\u304A\u3044\u3066\u306F\u3001umbral calculus \u3068\u306F\uFF08\u4E8C\u9805\u578B\u304A\u3088\u3073\u591A\u9805\u5F0F\u5217\u3092\u542B\u3080\uFF09\u30B7\u30A7\u30D5\u30A1\u30FC\u5217\u306E\u7814\u7A76\u3092\u6307\u3059\u8A00\u8449\u306B\u306A\u3063\u3066\u3044\u308B\u304C\u3001\u305D\u308C\u3089\u3082\u307E\u305F\u5BFE\u5FDC\u3059\u308B\u7CFB\u7D71\u7684\u306A\u548C\u5206\u5DEE\u5206\u5B66\u5468\u8FBA\u306E\u624B\u6CD5\u306B\u5305\u6442\u3055\u308C\u308B\u3002"@ja . . "\uC74C\uACC4\uC0B0\uBC95"@ko . . . . . . . . "In mathematics before the 1970s, the term umbral calculus referred to the surprising similarity between seemingly unrelated polynomial equations and certain \"shadowy\" techniques used to \"prove\" them. These techniques were introduced by John Blissard and are sometimes called Blissard's symbolic method. They are often attributed to \u00C9douard Lucas (or James Joseph Sylvester), who used the technique extensively."@en . . "Rachunek umbralny"@pl . . . . . . . "C\u00E1lculo umbral"@es . . . . "Umbral calculus"@en . . . "En math\u00E9matiques, le calcul ombral est le nom d'un ensemble de techniques de calcul formel qui, avant les ann\u00E9es 1970, \u00E9tait plut\u00F4t appel\u00E9 calcul symbolique. Il s'agit de l'\u00E9tude des similarit\u00E9s surprenantes entre certaines formules polynomiales a priori non reli\u00E9es entre elles, et d'un ensemble de r\u00E8gles de manipulation (au demeurant assez peu claires) pouvant \u00EAtre utilis\u00E9es pour les obtenir (mais non les d\u00E9montrer). Ces techniques furent introduites en 1861 par (en) (et sont parfois connues sous le nom de m\u00E9thode symbolique de Blissard), mais elles sont souvent attribu\u00E9es \u00E0 James Joseph Sylvester, qui les utilisa de mani\u00E8re extensive, ou \u00E0 \u00C9douard Lucas. On a parfois \u00E9galement employ\u00E9 le terme de calcul symbolique pour d\u00E9signer le calcul op\u00E9rationnel de Heaviside, mais les deux m\u00E9thodes"@fr . "1970\u5E74\u4EE3\u4EE5\u524D\u306E\u6570\u5B66\u306B\u304A\u3044\u3066 \"umbral calculus\"\uFF08\u9670\u5F71\u306E\u7B97\u6CD5\u3001\u9670\u8A08\u7B97\uFF08\u3044\u3093\u3051\u3044\u3055\u3093\uFF09\uFF09\u306F\u3001\u3042\u308B\u7A2E\u306E\u300C\u8A3C\u660E\u300D\u306B\u7528\u3044\u3089\u308C\u308B\u3042\u308B\u7A2E\u306E\u6697\u55A9\u7684\u624B\u6CD5\u3068\u3001\u305D\u308C\u3068\u306F\u4E00\u898B\u3057\u3066\u7121\u95A2\u4FC2\u306E\u306F\u305A\u306E\u591A\u9805\u5F0F\u65B9\u7A0B\u5F0F\u3068\u306E\u9593\u306B\u6A2A\u305F\u308F\u308B\u9A5A\u304F\u3079\u304D\u95A2\u4FC2\u306B\u3064\u3044\u3066\u3044\u3046\u3082\u306E\u3067\u3042\u3063\u305F\u3002\u3053\u308C\u3089\u306E\u624B\u6CD5\u306F \u3067\u5C0E\u5165\u3055\u308C\u305F\u3082\u306E\u3067\u3001\u30D6\u30EA\u30B5\u30FC\u30C9\u306E\u8A18\u53F7\u6CD5 (Blissard's symbolic method) \u3068\u547C\u3070\u308C\u308B\u3053\u3068\u3082\u3042\u308B\u3002\u7406\u8AD6\u306E\u5C55\u958B\u306B\u306F\u3001\u3053\u306E\u624B\u6CD5\u3092\u5E83\u304F\u7528\u3044\u305F\u30EA\u30E5\u30AB\uFF08\u3084\u30B7\u30EB\u30F4\u30A7\u30B9\u30BF\u30FC\uFF09\u306E\u8CA2\u732E\u3082\u3042\u308B\u3002 1930-40\u5E74\u4EE3\u306B\u306F umbral calculus \u306B\u53B3\u683C\u306A\u8DB3\u5834\u3092\u7BC9\u304F\u3053\u3068\u3092\u8A66\u307F\u305F\u3002 1970\u5E74\u4EE3\u306B\u3001\u3001\u30B8\u30E3\u30F3\u30FB\u30AB\u30EB\u30ED\u30FB\u30ED\u30BF\u3089\u306F\u3001\u591A\u9805\u5F0F\u304B\u3089\u306A\u308B\u7A7A\u9593\u4E0A\u306E\u7DDA\u578B\u6C4E\u51FD\u6570\u3092\u7528\u3044\u3066 umbral calculus \u3092\u5C55\u958B\u3057\u305F\u3002\u73FE\u5728\u306B\u304A\u3044\u3066\u306F\u3001umbral calculus \u3068\u306F\uFF08\u4E8C\u9805\u578B\u304A\u3088\u3073\u591A\u9805\u5F0F\u5217\u3092\u542B\u3080\uFF09\u30B7\u30A7\u30D5\u30A1\u30FC\u5217\u306E\u7814\u7A76\u3092\u6307\u3059\u8A00\u8449\u306B\u306A\u3063\u3066\u3044\u308B\u304C\u3001\u305D\u308C\u3089\u3082\u307E\u305F\u5BFE\u5FDC\u3059\u308B\u7CFB\u7D71\u7684\u306A\u548C\u5206\u5DEE\u5206\u5B66\u5468\u8FBA\u306E\u624B\u6CD5\u306B\u5305\u6442\u3055\u308C\u308B\u3002"@ja . . . . "\uC870\uD569\uB860\uC5D0\uC11C \uC74C\uACC4\uC0B0\uBC95(\u9670\u8A08\u7B97\u6CD5, \uC601\uC5B4: umbral calculus)\uC740 \uD2B9\uC815 \uC218\uC5F4 \u00B7 \uB2E4\uD56D\uC2DD\uC5F4\uC5D0\uC11C\uC758 \uC544\uB7AB\uCCA8\uC790\uB97C \uB9C8\uCE58 \uAC70\uB4ED\uC81C\uACF1\uCC98\uB7FC \uC5EC\uACA8 \uACC4\uC0B0\uD558\uB294 \uACC4\uC0B0\uBC95\uC774\uB2E4."@ko . . . . . . . . "Termin rachunek umbralny by\u0142 pierwotnie zwi\u0105zany z zaskakuj\u0105cymi podobie\u0144stwami pomi\u0119dzy pozornie niepowi\u0105zanymi r\u00F3wnaniami algebraicznymi i pewnymi niejasnymi technikami u\u017Cytymi w celu ich uzyskania (ale nie udowodnienia). Te techniki zosta\u0142y wprowadzone przez i s\u0105 czasami nazywane metod\u0105 symboliczn\u0105 Blissarda. Cz\u0119sto s\u0105 one przypisywane innym matematykom (\u00C9douard Lucas, James Joseph Sylvester), kt\u00F3rzy wykorzystywali te techniki ekstensywnie. W latach 30. i 40. XX wieku spr\u00F3bowa\u0142 stworzy\u0107 rygorystyczne podstawy rachunku umbralnego. W latach 70. XX wieku , Gian-Carlo Rota oraz inni rozwin\u0119li rachunek r\u00F3\u017Cniczkowy za pomoc\u0105 funkcja\u0142\u00F3w liniowych na przestrzeniach wielomian\u00F3w. Obecnie termin rachunek umbralny odnosi si\u0119 do bada\u0144 (w tym ci\u0105gi wielomianowe i ), ale mo\u017Ce objemowa\u0107 r\u00F3wnie\u017C techniki systematycznej korespondencji sko\u0144czonego rachunku r\u00F3\u017Cnicowego."@pl . . . "Roman"@en . . . "Umbral-Kalk\u00FCl"@de . . . . . . . "Em matem\u00E1tica, costumava-se utilizar o termo c\u00E1lculo umbral em refer\u00EAncia a surpreendentes similaridades entre equa\u00E7\u00F5es polinomiais e certas t\u00E9cnicas emp\u00EDricas utilizadas para 'demonstr\u00E1-las'. Tais t\u00E9cnicas foram apresentadas por John Blissard em 1861, sendo por vezes chamadas de m\u00E9todo simb\u00F3lico de Blissard. S\u00E3o eventualmente atribu\u00EDdas a \u00C9douard Lucas ou James Joseph Sylvester, que usaram estas t\u00E9cnicas extensivamente. Nas d\u00E9cadas de 1930 e 1940, Eric Temple Bell esfor\u00E7ou-se por estabelecer uma justificativa matem\u00E1tica rigorosa para o c\u00E1lculo umbral, sem lograr \u00EAxito completo."@pt . . . "214124"^^ . "Umbral Calculus"@en . . . "En math\u00E9matiques, le calcul ombral est le nom d'un ensemble de techniques de calcul formel qui, avant les ann\u00E9es 1970, \u00E9tait plut\u00F4t appel\u00E9 calcul symbolique. Il s'agit de l'\u00E9tude des similarit\u00E9s surprenantes entre certaines formules polynomiales a priori non reli\u00E9es entre elles, et d'un ensemble de r\u00E8gles de manipulation (au demeurant assez peu claires) pouvant \u00EAtre utilis\u00E9es pour les obtenir (mais non les d\u00E9montrer). Ces techniques furent introduites en 1861 par (en) (et sont parfois connues sous le nom de m\u00E9thode symbolique de Blissard), mais elles sont souvent attribu\u00E9es \u00E0 James Joseph Sylvester, qui les utilisa de mani\u00E8re extensive, ou \u00E0 \u00C9douard Lucas. On a parfois \u00E9galement employ\u00E9 le terme de calcul symbolique pour d\u00E9signer le calcul op\u00E9rationnel de Heaviside, mais les deux m\u00E9thodes n'ont que peu de points communs. Dans les ann\u00E9es 1930 et 1940, Eric Temple Bell essaya, sans grand succ\u00E8s, de donner des bases rigoureuses au calcul ombral. Dans les ann\u00E9es 1970, Steven Roman, Gian-Carlo Rota et d'autres d\u00E9velopp\u00E8rent le calcul ombral du point de vue des formes lin\u00E9aires sur les espaces de polyn\u00F4mes. Actuellement, le calcul ombral est ainsi compris comme l'\u00E9tude de certaines suites de polyn\u00F4mes, les suites de Sheffer, incluant les suites de polyn\u00F4mes de type binomial (li\u00E9es aux polyn\u00F4mes de Bell) et les suites d'Appell."@fr .