:''M. P. Appell is the same person: it stands for Monsieur Paul Appell''.
Paul Émile Appell (27 September 1855 in
Strasbourg
Strasbourg ( , ; ; ) is the Prefectures in France, prefecture and largest city of the Grand Est Regions of France, region of Geography of France, eastern France, in the historic region of Alsace. It is the prefecture of the Bas-Rhin Departmen ...
– 24 October 1930 in
Paris
Paris () is the Capital city, capital and List of communes in France with over 20,000 inhabitants, largest city of France. With an estimated population of 2,048,472 residents in January 2025 in an area of more than , Paris is the List of ci ...
) 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 of the
University of Paris
The University of Paris (), known Metonymy, metonymically as the Sorbonne (), was the leading university in Paris, France, from 1150 to 1970, except for 1793–1806 during the French Revolution. Emerging around 1150 as a corporation associated wit ...
.
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
École or Ecole may refer to:
* an elementary school in the French educational stages normally followed by Secondary education in France, secondary education establishments (collège and lycée)
* École (river), a tributary of the Seine flowing i ...
in 1873.
He was elected to the
French Academy of Sciences
The French Academy of 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 method, scientific research. It was at the forefron ...
in 1892.
In 1895, he became a Professor at the
École Centrale Paris
École or Ecole may refer to:
* an elementary school in the French educational stages normally followed by Secondary education in France, secondary education establishments (collège and lycée)
* École (river), a tributary of the Seine flowing i ...
. 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 people, French mathematician and politician. As a mathematician, he was known for his founding work in the areas of measure theory and probability.
Biograp ...
, 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 (''p ...
in the line of Chasles, then on algebraic functions, differential equations, 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 algebraic ...
. Appell was the editor of the collected works of Henri Poincaré
Jules Henri Poincaré (, ; ; 29 April 185417 July 1912) was a French mathematician, Theoretical physics, theoretical physicist, engineer, and philosophy of science, philosopher of science. He is often described as a polymath, and in mathemati ...
. 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, that generalize Gauss
Johann Carl Friedrich Gauss (; ; ; 30 April 177723 February 1855) was a German mathematician, astronomer, Geodesy, geodesist, and physicist, who contributed to many fields in mathematics and science. He was director of the Göttingen Observat ...
's hypergeometric series
In mathematics, the Gaussian or ordinary hypergeometric function 2''F''1(''a'',''b'';''c'';''z'') is a special function represented by the hypergeometric series, that includes many other special functions as specific or limiting cases. It is ...
.
He established the set of partial differential equations
In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives.
The function is often thought of as an "unknown" that solves the equation, similar to how ...
of which these functions are solutions, and found formulas and expressions of these series in terms of hypergeometric series
In mathematics, the Gaussian or ordinary hypergeometric function 2''F''1(''a'',''b'';''c'';''z'') is a special function represented by the hypergeometric series, that includes many other special functions as specific or limiting cases. It is ...
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 device made of a weight suspended from a pivot so that it can swing freely. When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate i ...
.
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 (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
Édouard Jean-Baptiste Goursat (21 May 1858 – 25 November 1936) was a French mathematician, now remembered principally as an expositor for his ''Cours d'analyse mathématique'', which appeared in the first decade of the twentieth century. It s ...
.
* 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
See also
* Abelian integral
* Generalized Appell polynomials
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'École Normale Supérieure
École or Ecole may refer to:
* an elementary school in the French educational stages normally followed by Secondary education in France, secondary education establishments (collège and lycée)
* École (river), a tributary of the Seine flowing i ...
2e 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
{{DEFAULTSORT:Appell, Paul Emile
1855 births
1930 deaths
Scientists from Strasbourg
French atheists
19th-century French mathematicians
20th-century French mathematicians
French geometers
French mathematical analysts
École Normale Supérieure alumni
Academic staff of the University of Paris
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