Christian Houzels "The Work of Niels Henrik Abel" er publisert i boken "The Legacy of Niels Henrik Abel" som inneholder en rekke vitenskaplige skrifter om emner som relaterer seg til Niels Henrik Abels verker, skrevet av noen av de fremste spesialistene på feltet.
The Work of Niels Henrik Abel
Av 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.
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- 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