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What is Complex Elliptic Functions Explained about?

Elliptic functions are usually studied as functions of real variables, but examining them as functions of complex variables reveals their true power and nature. Jacobi introduced the "imaginary transformation", which relates the elliptic functions of a purely imaginary argument to those of a real argument. This transformation defines the elliptic functions for all complex arguments and shows that they are doubly periodic, in contrast to circular functions which are only singly periodic. The addition formula

Author

dawson zhao

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EN