Désiré André

Antoine Désiré André (born March 29, 1840 in Lyon , † September 12, 1917 in Paris ) was a French mathematician who dealt with analytical combinatorics . He was a student of Joseph Bertrand and taught as a professor at the Institut Catholique de Paris . He became famous for his work on alternating permutations and the principle of reflection .

Life

André first went to school at the Lycée de Lyon . In his last year of school he moved to the renowned Lycée Henri IV in Paris , where he graduated as the best in his class in 1860. He then studied at the École normal supérieure in Paris in the natural sciences section. In 1863 he received his agrégation in mathematics. He completed his doctorate in mathematics in 1877 with the work Développements en séries des fonctions elliptiques et de leurs puissances (series development of elliptic functions and their powers).

After completing his studies, he taught elementary mathematics at the Lycée de Troyes and the École des Carmes , and later special mathematics at the Collège Sainte-Barbe and the Collège Stanislas in Paris. He then taught applied mathematics at the natural science faculty of the University of Dijon before being appointed professor of mathematical analysis at the Institut Catholique de Paris in 1887 . He retired in 1907.

plant

André wrote a large number of scientific publications, especially in analytical combinatorics . He made important contributions to factorials , combinations , variations , permutations , inversions , recurrences , series , determinants , and various other combinatorial problems. Perhaps his best-known result is the representation of the Maclaurin series of secans - and the tangent function (1879, 1881) of form

{\ displaystyle \ sec x + \ tan x = \ sum _ {n = 0} ^ {\ infty} A_ {n} {\ frac {x ^ {n}} {n!}}}

,

where is the number of alternating permutations of length . A combinatorial variant of the reflection principle (1887), which Louis Bachelier later used in the analysis of Wiener processes in financial mathematics, goes back to him . ${\ displaystyle A_ {n}}$ ${\ displaystyle n}$

Honors

In 1889 he became president of the Société Mathématique de France . In July 1897 he was made a Knight of the French Legion of Honor ( Chevalier de la Légion d'Honneur ). In 1904 he received the Prix Poncelet of the Académie des Sciences .

Publications

Books

Désiré André: L'arithmétique des écoles primaires: Cours élémentaire . Vve E. Belin et fils, 1883.
Désiré André: L'arithmétique des écoles primaires: Cours moyen . Vve E. Belin et fils, 1884.
Désiré André: L'arithmétique des écoles primaires: Cours supérieur . Vve E. Belin et fils, 1889.
Désiré André: Des notations mathématiques: Enumération, choix et usage . Gauthier-Villars, 1909.
Désiré André: Notice sur les travaux scientifiques . Gauthier-Villars, 1910.

Article (selection)

Désiré André: Développements en séries des fonctions elliptiques et de leurs puissances . In: Annales scientifiques de l'École Normale Supérieure . tape 6 , 1877, p. 265-328 .
Désiré André: Développements de sec x et tan x . In: Comptes Rendus de l'Académie des Sciences . tape 88 , 1879, pp. 965-967 .
Désiré André: Mémoire sur les permutations alternées . In: J. Math . tape 7 , 1881, p. 167-184 .
Désiré André: Solution directed you problem résolu par M. Bertrand . In: Comptes Rendus de l'Académie des Sciences . tape 105 , 1887, pp. 436-437 .

Web links

Catalog raisonné at MathDoc, University of Joseph Fourier Grenoble I
Author profile in the database zbMATH

Individual evidence

^ ^A ^b ^c ^d Henry Carnoy: Dictionnaire Biographique International Des Ecrivains . Georg Olms, 1987, ISBN 3-487-41058-3 , pp. 121 .
^ Philippe Flajolet , Robert Sedgewick : Analytic Combinatorics . Cambridge University Press, 2009, ISBN 1-139-47716-1 , pp. 2 .
^ Mark Davis, Alison Etheridge: Louis Bachelier's Theory of Speculation: The Origins of Modern Finance . Princeton University Press, 2011, ISBN 1-4008-2930-5 , pp. 90 .
↑ Bruno de Finetti: Probability theory: introductory synthesis with critical appendix . Oldenbourg, 1981, ISBN 3-486-44701-7 , pp. 496-497 .
↑ Anne-Marie Decaillot, Klaus Volkert: Cantor and the French: mathematics, philosophy and the infinite . Springer, 2011, ISBN 3-642-14869-7 , pp. 49 .

personal data
SURNAME	André, Désiré
ALTERNATIVE NAMES	André, Antoine Désiré (full name)
BRIEF DESCRIPTION	French mathematician
DATE OF BIRTH	March 29, 1840
PLACE OF BIRTH	Lyon
DATE OF DEATH	September 12, 1917
Place of death	Paris

[carnoy-1] A ^b ^c ^d Henry Carnoy: Dictionnaire Biographique International Des Ecrivains . Georg Olms, 1987, ISBN 3-487-41058-3 , pp. 121 .

[2] Philippe Flajolet , Robert Sedgewick : Analytic Combinatorics . Cambridge University Press, 2009, ISBN 1-139-47716-1 , pp. 2 .

[3] Mark Davis, Alison Etheridge: Louis Bachelier's Theory of Speculation: The Origins of Modern Finance . Princeton University Press, 2011, ISBN 1-4008-2930-5 , pp. 90 .

[4] Bruno de Finetti: Probability theory: introductory synthesis with critical appendix . Oldenbourg, 1981, ISBN 3-486-44701-7 , pp. 496-497 .

[5] Anne-Marie Decaillot, Klaus Volkert: Cantor and the French: mathematics, philosophy and the infinite . Springer, 2011, ISBN 3-642-14869-7 , pp. 49 .