54 research outputs found
Note sur le développement des fonctions en séries ordonnées suivant les puissances ascendantes des variables
Sur la sommation de certaines puissances d'une racine primitive d'une équation binÎme, et en particulier, des puissances qui offrent pour exposants les résidus cubiques inférieurs au module donné
Méthode simple et nouvelle pour la détermination complÚte des sommes alternées formées avec les racines primitives des équations binomes
Basel Problem â Preliminaries
SummaryIn the article we formalize in the Mizar system [4] preliminary facts needed to prove the Basel problem [7, 1]. Facts that are independent from the notion of structure are included here.KorniĆowicz Artur - Institute of Informatics, University of BiaĆystok, PolandPÄ
k Karol - Institute of Informatics, University of BiaĆystok, PolandM. Aigner and G. M. Ziegler. Proofs from THE BOOK. Springer-Verlag, Berlin Heidelberg New York, 2004.Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41â46, 1990.Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107â114, 1990.Grzegorz Bancerek, CzesĆaw ByliĆski, Adam Grabowski, Artur KorniĆowicz, Roman Matuszewski, Adam Naumowicz, Karol PÄ
k, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261â279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi: 10.1007/978-3-319-20615-817.CzesĆaw ByliĆski. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529â536, 1990.CzesĆaw ByliĆski. Functions and their basic properties. Formalized Mathematics, 1(1): 55â65, 1990.Augustin Louis Cauchy. Cours dâanalyse de lâEcole royale polytechnique. de lâImprimerie royale, 1821.Wenpai Chang, Yatsuka Nakamura, and Piotr Rudnicki. Inner products and angles of complex numbers. Formalized Mathematics, 11(3):275â280, 2003.Wenpai Chang, Hiroshi Yamazaki, and Yatsuka Nakamura. The inner product and conjugate of finite sequences of complex numbers. Formalized Mathematics, 13(3):367â373, 2005.Noboru Endou. Double series and sums. Formalized Mathematics, 22(1):57â68, 2014. doi: 10.2478/forma-2014-0006.Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Definition of integrability for partial functions from â to â and integrability for continuous functions. Formalized Mathematics, 9(2):281â284, 2001.Adam Grabowski and Yatsuka Nakamura. Some properties of real maps. Formalized Mathematics, 6(4):455â459, 1997.Artur KorniĆowicz and Yasunari Shidama. Inverse trigonometric functions arcsin and arccos. Formalized Mathematics, 13(1):73â79, 2005.JarosĆaw Kotowicz. Partial functions from a domain to the set of real numbers. Formalized Mathematics, 1(4):703â709, 1990.Xiquan Liang and Bing Xie. Inverse trigonometric functions arctan and arccot. Formalized Mathematics, 16(2):147â158, 2008. doi: 10.2478/v10037-008-0021-3.Robert Milewski. Trigonometric form of complex numbers. Formalized Mathematics, 9 (3):455â460, 2001.Keiichi Miyajima and Takahiro Kato. The sum and product of finite sequences of complex numbers. Formalized Mathematics, 18(2):107â111, 2010. doi: 10.2478/v10037-010-0014-x.Cuiying Peng, Fuguo Ge, and Xiquan Liang. Several integrability formulas of special functions. Formalized Mathematics, 15(4):189â198, 2007. doi: 10.2478/v10037-007-0023-6.Konrad Raczkowski. Integer and rational exponents. Formalized Mathematics, 2(1):125â130, 1991.Konrad Raczkowski and PaweĆ Sadowski. Real function continuity. Formalized Mathematics, 1(4):787â791, 1990.Piotr Rudnicki and Andrzej Trybulec. Abianâs fixed point theorem. Formalized Mathematics, 6(3):335â338, 1997.Yasunari Shidama, Noboru Endou, and Katsumi Wasaki. Riemann indefinite integral of functions of real variable. Formalized Mathematics, 15(2):59â63, 2007. doi: 10.2478/v10037-007-0007-6.Andrzej Trybulec and CzesĆaw ByliĆski. Some properties of real numbers. Formalized Mathematics, 1(3):445â449, 1990.MichaĆ J. Trybulec. Integers. Formalized Mathematics, 1(3):501â505, 1990.Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73â83, 1990.Yuguang Yang and Yasunari Shidama. Trigonometric functions and existence of circle ratio. Formalized Mathematics, 7(2):255â263, 1998.25214114
A. L. Cauchy's Vorlesungen ĂŒber die Differenzialrechnung, mit Fourier's Auflösungsmethode der bestimmten Gleichungen verbunden
[A. L. Cauchy] ; aus dem Franz. ĂŒbers. von C. H. SchnuseExlibrisstempel: "R. Wolf" 002281305_0001 Exemplar der ETH-BI
Analyse algébrique
par Augustin-Louis Cauchykeine weiteren BĂ€nde erschienenHandschriftliches Exlibris: "H. Pfaff" 010171279_0002 Exemplar der ETH-BIBHandschriftliches Exlibris: "C. Arnold" 010171279_0001 Exemplar der ETH-BI
Mémoire sur la résolution des équations numériques et sur la théorie de l'élimination
par Augustin-Louis Cauch
Kiri P. H. Fuss'ile
Cauchy, Augustin Louis, 1789-1857, prantsuse matemaatik, Peterburi TA liigeFuss, Paul Heinrich, 1798-1855, matemaatik, Peterburi TA sekretÀrSaadab akadeemiale kaks töö
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