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Research on elliptic functions. (Recherches sur les fonctions elliptiques.) (French) ERAM 002.0052cj
This is the first part of Abel’s great memoir on elliptic functions. He begins by recalling the work by Euler, Lagrange and Legendre on elliptic integrals, then he defines functions \(\phi\), \(f\) and \(F\) by inverting such integrals, and states that the main aim of his memoir is solving the equation of degree \(m^2\) that holds when one expresses the values of \(\phi(mz)\), \(f(mz)\) and \(F(mz)\) in terms of \(\phi(z)\), \(f(z)\) and \(F(z)\). For a detailed summary of the contents of this article see [C. Houzel, in: The legacy of Niels Henrik Abel. Papers from the Abel bicentennial conference, University of Oslo, Oslo, Norway, 2002. Berlin: Springer. 21–177 (2004; Zbl 1077.01013), Section 6.].

33E05 Elliptic functions and integrals
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