Christian Houzel's "The Work of Niels Henrik Abel" was published in the book The Legacy of Niels Henrik Abel" which contains a series of research papers on subjects related to the work of Niels Henrik Abel, written by some of the foremost specialists in their fields.
The Legacy of Niels Henrik Abel - The Abel Bicentennial, Oslo 2002
Springer-Verlag 2004. (Editors O. A. Laudal and R. Piene)
The Work of Niels Henrik Abel
By Christian Houzel
During his short life, N. H. Abel devoted himself to several topics characteristic of the mathematics of his time. We note that, after an unsuccessful investigation of the influence of the Moon on the motion of a pendulum, he chose subjects in pure mathematics rather than in mathematical physics. It is possible to classify these subjects in the following way:
- solution of algebraic equations by radicals;
- new transcendental functions, in particular elliptic integrals, elliptic functions, abelian integrals;
- functional equations;
- integral transforms;
- theory of series treated in a rigourous way.
The first two topics are the most important and the best known, but we shall see that there are close links between all the subjects in Abel's treatment.
To read more, please download the pdf version of Christian Houzel's "The Work of Niels Henrik Abel".
- Functional Equations
- Integral Transforms and Definite Integrals
- Algebraic Equations
- Hyperelliptic Integrals
- Abel Theorem
- Elliptic functions
- Development of the Theory of Transformation of Elliptic Functions
- Further Development of the Theory of Elliptic Functions and Abelian Integrals