mathematics

Paul Émile Appell

Paul Émile Appell is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Paul Émile Appell rather than just read about it. In short: M. P.

Key takeaways

Paul Émile Appell belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Paul Émile Appell to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Paul Émile Appell from memory before moving on to harder problems.

Reference excerpt

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) 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. 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. He was awarded Order of the White Eagle. and was also elected to honorary membership of the Manchester Literary and Philosophical Society.

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.

Appell series He introduced a set of four hypergeometric series F1, F2, F3, F4 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, 1893–1896) 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) [1], 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 the French National Library for a more detailed list

Illustrations

Worked examples

Example 1 — a first encounter with Paul Émile Appell

Start with the simplest possible case. Write down what Paul Émile Appell claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Paul Émile Appell before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Paul Émile Appell ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Paul Émile Appell

In research: Paul Émile Appell appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Paul Émile Appell in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Paul Émile Appell is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1855 births, 1930 deaths, 19th-century French mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Paul Émile Appell outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Paul Émile Appell in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Paul Émile Appell means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Paul Émile Appell out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Paul Émile Appell in simple terms?

M. P.

Why does Paul Émile Appell matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Paul Émile Appell?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Paul Émile Appell.