Paul Émile Appell
Encyclopedia
Paul Appell also known as Paul Émile Appel, was a French
mathematician
and Rector
of the University of Paris
. The concept of Appell polynomials is named after him, as is rue Paul Appell in the 14th arrondissement of Paris.
in 1873.
He was elected to the French Academy of Sciences
in 1892.
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.
His daughter Marguerite Appell (1883–1969), who married the mathematician Émile Borel
, is known as a novelist under her pen-name Camille Marbo.
in the line of Chasles
, then on algebraic function
s, differential equation
s, and complex analysis
.
, 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.
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
.
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
and Rector
Rector
The word rector has a number of different meanings; it is widely used to refer to an academic, religious or political administrator...
of the University of Paris
University of Paris
The University of Paris was a university located in Paris, France and one of the earliest to be established in Europe. It was founded in the mid 12th century, and officially recognized as a university probably between 1160 and 1250...
. The concept of Appell polynomials is named after him, as is rue Paul Appell in the 14th arrondissement of Paris.
Life
Paul Appell entered the École Normale SupérieureÉcole Normale Supérieure
The École normale supérieure is one of the most prestigious French grandes écoles...
in 1873.
He was elected to the French Academy of Sciences
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 research...
in 1892.
Between 1903 and 1920 he was Dean
Dean (education)
In academic administration, a dean is a person with significant authority over a specific academic unit, or over a specific area of concern, or both...
of the Faculty of Science of the University of Paris, then Rector of the University of Paris from 1920 to 1925.
His daughter Marguerite Appell (1883–1969), who married the mathematician Émile Borel
Émile Borel
Félix Édouard Justin Émile Borel was a French mathematician and politician.Borel was born in Saint-Affrique, Aveyron. Along with René-Louis Baire and Henri Lebesgue, he was among the pioneers of measure theory and its application to probability theory. The concept of a Borel set is named in his...
, is known as a novelist under her pen-name Camille Marbo.
Work
He worked first on projective geometryProjective geometry
In mathematics, projective geometry is the study of geometric properties that are invariant under projective transformations. This means that, compared to elementary geometry, projective geometry has a different setting, projective space, and a selective set of basic geometric concepts...
in the line of Chasles
Michel Chasles
Michel Floréal Chasles was a French mathematician.He was born at Épernon in France and studied at the École Polytechnique in Paris under Siméon Denis Poisson. In the War of the Sixth Coalition he was drafted to fight in the defence of Paris in 1814...
, then on algebraic function
Algebraic function
In mathematics, an algebraic function is informally a function that satisfies a polynomial equation whose coefficients are themselves polynomials with rational coefficients. For example, an algebraic function in one variable x is a solution y for an equationwhere the coefficients ai are polynomial...
s, differential equation
Differential equation
A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders...
s, and complex analysis
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 useful in many branches of mathematics, including number theory and applied mathematics; as well as in physics,...
.
Appell series
He has introduced a set of four hypergeometric series F1, F2, F3, F4 of two variables, now called Appell seriesAppell series
In mathematics, Appell series are a set of four hypergeometric series F1, F2, F3, F4 of two variables that were introduced by and that generalize Gauss's hypergeometric series 2F1 of one variable...
, that generalize Gauss
Gauss
Gauss may refer to:*Carl Friedrich Gauss, German mathematician and physicist*Gauss , a unit of magnetic flux density or magnetic induction*GAUSS , a software package*Gauss , a crater on the moon...
's hypergeometric series
Hypergeometric series
In mathematics, a generalized hypergeometric series is a series in which the ratio of successive coefficients indexed by n is a rational function of n. The series, if convergent, defines a generalized hypergeometric function, which may then be defined over a wider domain of the argument by...
.
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
Hypergeometric series
In mathematics, a generalized hypergeometric series is a series in which the ratio of successive coefficients indexed by n is a rational function of n. The series, if convergent, defines a generalized hypergeometric function, which may then be defined over a wider domain of the argument by...
of one variable. In 1926, with Professor Joseph-Marie Kampé de Fériet
Joseph Kampé de Fériet
Marie-Joseph Kampé de Fériet was professor at Université Lille Nord de France from 1919 to 1969...
, he authored a treatise on generalized hypergeometric series.
Mechanics
In mechanics, he proposed an alternative formulation of analytical mechanics known asAppell's equation of motion.
He discovered a physical interpretation of the imaginary
Imaginary number
An imaginary number is any number whose square is a real number less than zero. When any real number is squared, the result is never negative, but the square of an imaginary number is always negative...
period
Periodic function
In mathematics, a periodic function is a function that repeats its values in regular intervals or periods. The most important examples are the trigonometric functions, which repeat over intervals of length 2π radians. Periodic functions are used throughout science to describe oscillations,...
of the doubly periodic function whose restriction to real
Real number
In mathematics, a real number is a value that represents a quantity along a continuum, such as -5 , 4/3 , 8.6 , √2 and π...
arguments describes the motion of an ideal pendulum
Pendulum (mathematics)
The mathematics of pendulums are in general quite complicated. Simplifying assumptions can be made, which in the case of a simple pendulum allows the equations of motion to be solved analytically for small-angle oscillations.- Simple gravity pendulum :...
.
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 HadamardJacques HadamardJacques Salomon Hadamard FRS was a French mathematician who made major contributions in number theory, complex function theory, differential geometry and partial differential equations.-Biography:...
(C. Hérissey, Évreux, 1899) - Éléments de la théorie des vecteurs et de la géométrie analytique (Payot, 1926)
- 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)
- Souvenirs d'un alsacien , autobiographic (Payot, 1923)
- Théorie des fonctions algébriques et de leurs intégrales with Edouard GoursatEdouard GoursatÉdouard Jean-Baptiste Goursat 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 set a standard for the high-level teaching of mathematical analysis, especially complex analysis...
. - Fonctions hypergéométriques et hypersphériques with Joseph-Marie Kampé de Fériet (Gauthier-Villars, 1926)
- See catalogue of the French National Library for a more detailed list
See also
- Generalized Appell polynomials
- Appell sequence
- Appell–Lerch sum
- Appell–Humbert theoremAppell–Humbert theoremIn mathematics, the Appell–Humbert theorem describes the line bundles on a complex torus or complex abelian variety.It was proved for 2-dimensional tori by and .-Statement:...
External Links
- (fr:) E. Lebon, Biographie et bibliographie analytique des écrits de Paul Appell at Project Gutenberg.