On Jacobi's transformation theory of elliptic functions (Q461376)

The modern theory of elliptic functions was created during a historical race between Abel and Jacobi. Whereas the publications of Abel have been studied extensively (see, e.g. [\textit{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)]), Jacobi's work, which is a lot more difficult to read than Abel's (Jacobi's presentation is not as clear as Abel's, and he wrote in Latin) has to a large degree been neglected. In this article, the question is discussed how Jacobi may have discovered the transformation formulas he first presented in 1827.