The Work of Niels Henrik Abel

Christian Houzel

A chapter in The Legacy of Niels Henrik Abel, 2004, pp 21-177 from Springer

Abstract: 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 radicals 2. new transcendental functions, in particular elliptic integrals, elliptic functions, abelian integrals 3. functional equations 4. integral transforms 5. theory of series treated in a rigourous way.

Keywords: Rational Function; Elliptic Function; Algebraic Function; Elliptic Integral; Addition Theorem (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-18908-1_4

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DOI: 10.1007/978-3-642-18908-1_4

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