SWhat changed
Inverse-amplitude functions, complementary-modulus/imaginary-argument relations and H/theta quotients organize a coherent elliptic-function representation framework.
Scientific scope
Inverse-amplitude functions, complementary-modulus/imaginary-argument relations and H/theta quotients organize a coherent elliptic-function representation framework. The target is the 1829 elliptic-function representation framework, with nondegenerate modulus and well-defined elliptic integrals. It is not all prior addition formulas, the later general theory of Abelian functions or rational functions of the complex argument. The account follows the selected translation and original Latin source. A reconstruction of all transformation proofs, exact constants, four-square arithmetic consequences and modern global analytic certification is outside its scope.
Evidence
Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.
Contributors
- Carl Gustav Jacob Jacobi · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.
- C. G. J. Jacobi, Fundamenta Nova Theoriae Functionum Ellipticarum (1829), Alexander Aycock English translation, Euler-Kreis Mainz
- C. G. J. Jacobi, Fundamenta Nova Theoriae Functionum Ellipticarum, Regiomonti: Bornträger,1829; ETH Rar 5081 original Latin OCR
Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.
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