The Work of Niels Henrik Abel

Abstract

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:1.solution of algebraic equations by radicals2.new transcendental functions, in particular elliptic integrals, elliptic functions, abelian integrals3.functional equations4.integral transforms5.theory of series treated in a rigourous way.