{{Short description|French mathematician (1855–1930)}} :'''''M. P. Appell''' is the same person: it stands for Monsieur Paul Appell''. {{Infobox scientist | name = Paul Appell | box_width = | image = Paul Appell-Portrait-1921.jpg | image_size = 190px | caption = Appell in 1921 | birth_date = {{Birth date|df=yes|1855|9|27}} | death_date = {{Death date and age|df=yes|1930|10|24|1855|9|27}} | birth_place = Strasbourg, France | death_place = Paris, France | field = Mathematics <br/> Physics | thesis_title = Sur les propriétés des cubiques gauches et le mouvement hélicoïdal d'un corps solide | thesis_url = https://patrimoine.sorbonne-universite.fr/idurl/1/1825 | thesis_year = 1876 | known_for = Appell polynomials<br>Appell series<br>Appell sequence<br/>Appell's equation of motion<br>Appell–Humbert theorem<br>Appell–Lerch sums<br>Complex–shift method | notable_students = | prizes = }} '''Paul Émile Appell''' (27 September 1855 in Strasbourg – 24 October 1930 in Paris) was a French mathematician and Rector of the University of Paris. Appell polynomials and Appell's equations of motion are named after him, as is rue Paul Appell in the 14th arrondissement of Paris and the minor planet 988 Appella.

==Life== Paul Appell entered the École Normale Supérieure in 1873. He was elected to the French Academy of Sciences in 1892.

In 1895, he became a Professor at the École Centrale Paris. Between 1903 and 1920 he was Dean of the Faculty of Science of the University of Paris, then Rector of the University of Paris from 1920 to 1925.

Appell was the President of the Société astronomique de France (SAF), the French astronomical society, from 1919 to 1921.<ref name=BSAF1937>[https://gallica.bnf.fr/ark:/12148/bpt6k96721072/f535.item.r=APPELL''Bulletin de la Société astronomique de France'', November 1937, plates X–IX]</ref>

His daughter Marguerite Appell (1883–1969), who married the mathematician Émile Borel, is known as a novelist under her pen-name Camille Marbo.

Appell was an atheist.<ref>MAUGIN, GRARD A. CONTINUUM MECHANICS THROUGH THE EIGHTEENTH AND NINETEENTH CENTURIES: historical perspectives ... from john bernoulli to ernst hellinger. Place of publication not identified: SPRINGER, 2016. Print. ""he was an atheist"</ref> He was awarded Order of the White Eagle.<ref>{{Cite book|last=Acović|first=Dragomir|title=Slava i čast: Odlikovanja među Srbima, Srbi među odlikovanjima|year=2012|location=Belgrade|publisher=Službeni Glasnik|pages=643}}</ref> and was also elected to honorary membership of the Manchester Literary and Philosophical Society.<ref>Memoirs and proceedings of the Manchester Literary & Philosophical Society FOURTH SERIES Eighth VOLUME 1894 </ref>

==Work== He worked first on projective geometry in the line of Chasles, then on algebraic functions, differential equations, and complex analysis. Appell was the editor of the collected works of Henri Poincaré. Jules Drach was co-editor of the first volume.<ref>{{cite journal|author=Birkhoff, G. D.|authorlink=George David Birkhoff|title=The Work of Poincaré on Differential Equations|journal=Bull. Amer. Math. Soc.|year=1934|volume=40|issue=5|pages=363–366|url=https://www.ams.org/journals/bull/1934-40-05/S0002-9904-1934-05835-X/S0002-9904-1934-05835-X.pdf|doi=10.1090/s0002-9904-1934-05835-x|doi-access=free}}</ref>

===Appell series=== He introduced a set of four hypergeometric series ''F''<sub>1</sub>, ''F''<sub>2</sub>, ''F''<sub>3</sub>, ''F''<sub>4</sub> of two variables, now called Appell series, that generalize Gauss's hypergeometric series.

He established the set of partial differential equations of which these functions are solutions, and found formulas and expressions of these series in terms of hypergeometric series of one variable. In 1926, with Professor Joseph-Marie Kampé de Fériet, he authored a treatise on generalized hypergeometric series.

===Mechanics=== In mechanics, he proposed an alternative formulation of analytical mechanics known as Appell's equation of motion.

He discovered a physical interpretation of the imaginary period of the doubly periodic function whose restriction to real arguments describes the motion of an ideal pendulum.

== Publications == * ''Traité de mécanique rationnelle'', 4 Vols. (Gauthier-Villars, 1893&ndash;1896) * [https://gallica.bnf.fr/ark:/12148/bpt6k290894 Traité de mécanique rationnelle Tome I] * [https://gallica.bnf.fr/ark:/12148/bpt6k29090b Traité de mécanique rationnelle Tome II] * [https://gallica.bnf.fr/ark:/12148/bpt6k29091p Traité de mécanique rationnelle Tome III] * [https://gallica.bnf.fr/ark:/12148/bpt6k290921 Traité de mécanique rationnelle Tome IV Fasc. 1] * [https://gallica.bnf.fr/ark:/12148/bpt6k29093c Traité de mécanique rationnelle Tome IV Fasc. 2] * [https://gallica.bnf.fr/ark:/12148/bpt6k29094q Traité de mécanique rationnelle Tome V]<ref>{{cite journal|author=Thomas, Tracy Yerkes|title=''Traité de Mécanique Rationnelle'', Vol. V|journal=Bull. Amer. Math. Soc.|year=1927|volume=33|issue=4|pages=493–495|url=https://www.ams.org/journals/bull/1927-33-04/S0002-9904-1927-04414-7/S0002-9904-1927-04414-7.pdf|doi=10.1090/s0002-9904-1927-04414-7|doi-access=free}}</ref> * [https://gallica.bnf.fr/ark:/12148/bpt6k82007h.image.f1.langFR Les mouvements de roulement en dynamique] with Jacques Hadamard (C. Hérissey, Évreux, 1899) * [https://gallica.bnf.fr/ark:/12148/bpt6k99648n.image Éléments de la théorie des vecteurs et de la géométrie analytique] (Payot, 1921) * [https://archive.org/details/elemdanalysemath00apperich Éléments d'analyse mathématique à l'usage des ingénieurs et des physiciens : cours professé à l'École centrale des arts et manufactures] (Gauthier-Villars, 1921) * [https://gallica.bnf.fr/ark:/12148/bpt6k995607.image.f1.langFR Principes de la théorie des fonctions elliptiques et applications] with E. Lacour (Gauthier-Villars, 1897) * [https://gallica.bnf.fr/ark:/12148/bpt6k38975w.image.f1.langFR Le problème géométrique des déblais et remblais] (Gauthier-Villars, 1928) * [https://gallica.bnf.fr/ark:/12148/bpt6k205234x.image ], autobiographic (Payot, 1923) * Théorie des fonctions algébriques et de leurs intégrales with Édouard Goursat.<ref>{{cite journal|author=Osgood, W. F.|authorlink=William Fogg Osgood|title=Review: ''Théorie des fonctions algébriques et de leurs intégrales'', par Paul Appell et Édouard Goursat|journal=Bull. Amer. Math. Soc.|year=1896|volume=2|issue=10|pages=317–327|url=https://www.ams.org/journals/bull/1896-02-10/S0002-9904-1896-00353-0/S0002-9904-1896-00353-0.pdf|doi=10.1090/s0002-9904-1896-00353-0|doi-access=free}}</ref> * Fonctions hypergéométriques et hypersphériques with Joseph-Marie Kampé de Fériet (Gauthier-Villars, 1926) *See catalogue of the [http://catalogue.bnf.fr/ French National Library] for a more detailed list

== See also == {{commons category|Paul Appell}} *Abelian integral *Generalized Appell polynomials

== References == {{reflist}} * (fr:) P. Appell, "Notice sur les travaux scientifiques" ''Acta Mathematica'' 45 (1925) pp.&nbsp;161–285. describes 257 of Appell's publications. * (fr:) E. Lebon, ''Biographie et bibliographie analytique des écrits de Paul Appell'' (Paris, 1910) * (fr:) P. Appell, "Sur une classe de polynômes", ''Annales scientifiques de l'École Normale Supérieure 2<sup>e</sup> série'', tome 9, 1880. * (fr:) P. Appell, "Sur les fonctions hypergeometriques de deux variables" [http://gallica.bnf.fr/ark:/12148/bpt6k1074460/f174.image Journal de Mathématiques Pures et Appliquées] series III,'''8''', 173 (1882). * (fr:) P. Appell, "Sur une interprétation des valeurs imaginaires du temps en Mécanique", ''Comptes Rendus Hebdomadaires des Scéances de l'Académie des Sciences'', volume 87, number 1, July, 1878. *{{Cite journal|title=Obituary Prof Paul Appell |journal=Nature |volume=126 |pages=924–925 |year=1930 |doi=10.1038/126924a0 |author=Greenwood, THOMAS |issue=3189 |doi-access=free }} * {{cite encyclopedia | last = May | first = Kenneth | title = Appell, Paul | encyclopedia = Dictionary of Scientific Biography | volume = 1 | pages = 193–195 | publisher = Charles Scribner's Sons | location = New York | year = 1970 | isbn = 978-0-684-10114-9 }} *{{MacTutor|id=Appell}}

==External links== * (fr:) E. Lebon, [http://www.gutenberg.org/ebooks/search.html/?format=html&default_prefix=all&sort_order=downloads&query=Paul+Appell ''Biographie et bibliographie analytique des écrits de Paul Appell''] at [https://web.archive.org/web/20060714134745/http://www.gutenberg.org/wiki/Main_Page Project Gutenberg]. * {{MathGenealogy|id=76440}} * [https://zbmath.org/authors/?q=ai:appell.paul Author profile] in the database zbMATH

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{{DEFAULTSORT:Appell, Paul Emile}} Category:1855 births Category:1930 deaths Category:Scientists from Strasbourg Category:French atheists Category:19th-century French mathematicians Category:20th-century French mathematicians Category:French geometers Category:French mathematical analysts Category:École normale supérieure (Paris) alumni Category:Academic staff of the University of Paris Category:Members of the French Academy of Sciences Category:Rectors of the University of Paris Category:Corresponding members of the Saint Petersburg Academy of Sciences Category:Corresponding Members of the Russian Academy of Sciences (1917–1925) Category:Honorary members of the Russian Academy of Sciences (1917–1925) Category:Honorary members of the USSR Academy of Sciences