:''M. P. Appell is the same person: it stands for Monsieur Paul Appell''. Paul Émile Appell (27 September 1855, in Strasbourg – 24 October 1930, in

Paris Paris () is the capital and most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), making it the 30th most densely populated city in the world in 2020. ...

) was a French

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

and

Rector Rector (Latin for the member of a vessel's crew who steers) may refer to: Style or title *Rector (ecclesiastical), a cleric who functions as an administrative leader in some Christian denominations *Rector (academia), a senior official in an edu ...

of the

University of Paris The University of Paris (french: link=no, Université de Paris), Metonymy, metonymically known as the Sorbonne (), was the leading university in Paris, France, active from 1150 to 1970, with the exception between 1793 and 1806 under the French Revo ...

Appell polynomials In mathematics, an Appell sequence, named after Paul Émile Appell, is any polynomial sequence \_ satisfying the identity :\frac p_n(x) = np_(x), and in which p_0(x) is a non-zero constant. Among the most notable Appell sequences besides the t ...

and Appell's equations of motion are named after him, as is rue Paul Appell in the

14th arrondissement of Paris The 14th arrondissement of Paris ( ), officially named ''arrondissement de l'Observatoire'' (; meaning "arrondissement of the Observatory", after the Paris Observatory), is one of the 20 arrondissements of the capital city of France. It is situa ...

and the minor planet

988 Appella 988 Appella, provisional designation , is a dark Themistian asteroid and slow rotator from the outer region of the asteroid belt, approximately 26 kilometers in diameter. It was discovered on 10 November 1922, by Russian–French astronomer Benj ...

Life

Paul Appell entered the

École Normale Supérieure École may refer to: * an elementary school in the French educational stages normally followed by secondary education Secondary education or post-primary education covers two phases on the International Standard Classification of Education sca ...

in 1873. He was elected to the

French Academy of Sciences The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research. It was at th ...

in 1892. In 1895, he became a Professor at the

École Centrale Paris École Centrale Paris (ECP; also known as École Centrale or Centrale) was a French grande école in engineering and science. It was also known by its official name ''École Centrale des Arts et Manufactures''. In 2015, École Centrale Paris mer ...

. 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.de la Société astronomique de France'', November 1937, plates X–IX
/ref> His daughter Marguerite Appell (1883–1969), who married the mathematician

Émile Borel Félix Édouard Justin Émile Borel (; 7 January 1871 – 3 February 1956) was a French mathematician and politician. As a mathematician, he was known for his founding work in the areas of measure theory and probability. Biography Borel was ...

, is known as a novelist under her pen-name Camille Marbo. Appell was an atheist. He was awarded Order of the White Eagle.

Work

He worked first on

projective geometry In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that, compared to elementary Euclidean geometry, projective geometry has a different setting, pr ...

in the line of Chasles, then on

algebraic function In mathematics, an algebraic function is a function that can be defined as the root of a polynomial equation. Quite often algebraic functions are algebraic expressions using a finite number of terms, involving only the algebraic operations additi ...

differential equation In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, a ...

s, and

complex analysis Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebra ...

. Appell was the editor of the collected works of

Henri Poincaré Jules Henri Poincaré ( S: stress final syllable ; 29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science. He is often described as a polymath, and in mathematics as "The ...

. Jules Drach was co-editor of the first volume.

Appell series

He introduced a set of four hypergeometric series ''F''₁, ''F''₂, ''F''₃, ''F''₄ of two variables, now called

Appell series In mathematics, Appell series are a set of four hypergeometric series ''F''1, ''F''2, ''F''3, ''F''4 of two variables that were introduced by and that generalize Gauss's hypergeometric series 2''F''1 of one variable. Appell established the set ...

, that generalize

Gauss Johann Carl Friedrich Gauss (; german: Gauß ; la, Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Sometimes refer ...

's hypergeometric series. He established the set of

partial differential equations In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similarly to ...

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 A pendulum is a weight suspended from a wikt:pivot, pivot so that it can swing freely. When a pendulum is displaced sideways from its resting, Mechanical equilibrium, equilibrium position, it is subject to a restoring force due to gravity that ...

Publications

* '' Traité de mécanique rationnelle'', 4 Vols. (Gauthier-Villars, 1893–1896)
Traité de mécanique rationnelle Tome I

Traité de mécanique rationnelle Tome II

Traité de mécanique rationnelle Tome III

Traité de mécanique rationnelle Tome IV Fasc. 1

Traité de mécanique rationnelle Tome IV Fasc. 2

Traité de mécanique rationnelle Tome V

Les mouvements de roulement en dynamique
with

Jacques Hadamard Jacques Salomon Hadamard (; 8 December 1865 – 17 October 1963) was a French mathematician who made major contributions in number theory, complex analysis, differential geometry and partial differential equations. Biography The son of a tea ...

(C. Hérissey, Évreux, 1899)
Éléments de la théorie des vecteurs et de la géométrie analytique
(Payot, 1921)
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)
Principes de la théorie des fonctions elliptiques et applications
with E. Lacour (Gauthier-Villars, 1897)
Le problème géométrique des déblais et remblais
(Gauthier-Villars, 1928)

autobiographic (Payot, 1923) * Théorie des fonctions algébriques et de leurs intégrales with Édouard Goursat. * Fonctions hypergéométriques et hypersphériques with Joseph-Marie Kampé de Fériet (Gauthier-Villars, 1926) *See catalogue of th
French National Library
for a more detailed list

References

* (fr:) P. Appell, "Notice sur les travaux scientifiques" ''Acta Mathematica'' 45 (1925) pp. 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'

2^e série'', tome 9, 1880. * (fr:) P. Appell, "Sur les fonctions hypergeometriques de deux variables
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. * * *

External links

* (fr:) E. Lebon
''Biographie et bibliographie analytique des écrits de Paul Appell''
a
Project Gutenberg
*
Author profile
in the database

zbMATH zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Information Infrastructur ...

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