Article ID: CBB001202205

On Jacobi’s Transformation Theory of Elliptic Functions (2014)


The main interpretative challenge set by the Fundamenta Nova Theoriae Functionum Ellipticarum lies in Jacobi’s transformation theory upon which the entire theoretical edifice of the treatise depends. Unfortunately, Jacobi did not convey any indication of how he attained his general formulae for rational transformations of elliptic functions. He limited himself to providing a posteriori verification of the validity of his claims. The aim of this paper is precisely to describe the heuristic path by which in 1827 Jacobi succeeded in finding these transformation formulae. The proposed historical reconstruction will hopefully shed new light upon the emergence in Jacobi’s work of the inversion process of elliptic integrals of the first kind and thus of the elliptic function sinam u itself.

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Authors & Contributors
Galuzzi, Massimo
Del Centina, Andrea
Fraser, Craig G.
Nakane, Michiyo
Kaplan, Pierre
Pieper, Herbert
Archive for History of Exact Sciences
Centaurus: International Magazine of the History of Mathematics, Science, and Technology
NTM: Zeitschrift für Geschichte der Naturwissenschaften, Technik und Medizin
Historia Mathematica
Historia Scientiarum: International Journal of the History of Science Society of Japan
Studies in History and Philosophy of Science
Oxford University Press
Springer International Publishing
Discovery in science
Equations and formulae
Methodology of science; scientific method
Jacobi, Karl Gustav Jakob
Darwin, Charles Robert
Galois, Évariste
Abel, Niels Henrik
Hamilton, William Rowan
Pell, John
Time Periods
19th century
18th century
20th century, early
17th century
20th century
United States
Universität Wien
Deutsche Akademie der Wissenschaften, Berlin

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