:''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 city, capital and List of communes in France with over 20,000 inhabitants, 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), ma ...

) 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, structure, space, models, and change. History On ...

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 , image_name = Coat of arms of the University of Paris.svg , image_size = 150px , caption = Coat of Arms , latin_name = Universitas magistrorum et scholarium Parisiensis , motto = ''Hic et ubique terrarum'' (Latin) , mottoeng = Here and a ...

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.

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 establishments (collège and lycée) * École (river), a tributary of the Seine flowing in région Île-de-France * École, S ...

in 1873. He was elected to the French Academy of Sciences 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 Dean may refer to: People * Dean (given name) * Dean (surname), a surname of Anglo-Saxon English origin * Dean (South Korean singer), a stage name for singer Kwon Hyuk * Dean Delannoit, a Belgian singer most known by the mononym Dean Titles * ...

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 Marguerite Borel known as Camille Marbo (11 April 1883 – 5 February 1969) ''née'' Marguerite Appell, was a 20th-century French writer, president and laureate of the Prix Femina in 1913 and president of the Société des gens de lettres. ...

. 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, ...

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, an ...

s, and complex analysis. Appell was the editor of the collected works of Henri Poincaré. 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 (; 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 Period may refer to: Common uses * Era, a length or span of time * Full stop (or period), a punctuation mark Arts, entertainment, and media * Period (music), a concept in musical composition * Periodic sentence (or rhetorical period), a concept ...

of the

doubly periodic function In mathematics, a doubly periodic function is a function defined on the complex plane and having two "periods", which are complex numbers ''u'' and ''v'' that are linearly independent as vectors over the field of real numbers. That ''u'' and '' ...

whose restriction to

real Real may refer to: Currencies * Brazilian real (R$) * Central American Republic real * Mexican real * Portuguese real * Spanish real * Spanish colonial real Music Albums * ''Real'' (L'Arc-en-Ciel album) (2000) * ''Real'' (Bright album) (2010) ...

arguments describes the motion of an ideal

pendulum A pendulum is 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 it back toward th ...

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 teac ...

(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 se ...

. * 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 Infrastruct ...

{{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