Abstract
This chapter considers how elliptic functions and complex functions were first brought together. This was an important step for both subjects, which, as Jacobi noted in his lectures, seemed to be kept apart by the complications resulting from the two-valued nature of the integrand in the elliptic integrals.
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Notes
- 1.
See Lützen (1990, Chap. 13)
- 2.
As Lützen has pointed out out in his analysis of Liouville’s work, (1990), Liouville’s argument extends readily to any doubly periodic complex function.
- 3.
See Lützen (1990, Chap. 13).
- 4.
In an otherwise faithful publication he chose to replace Liouville’s original proof with one of his own, based on the calculus of residues, as he said in an introductory footnote.
- 5.
The mathematician who pioneered this route successfully was Weierstrass in the 1860s.
- 6.
See Bottazzini and Gray (2013, 4.6).
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Gray, J. (2015). Complex Functions and Elliptic Integrals. In: The Real and the Complex: A History of Analysis in the 19th Century. Springer Undergraduate Mathematics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-23715-2_11
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DOI: https://doi.org/10.1007/978-3-319-23715-2_11
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