I What are the definitions of Jacobi Elliptic Functions?

AI Thread Summary
Jacobi elliptic functions, such as sn(z), are generalizations of trigonometric functions that describe motion along an ellipse rather than a circle. These functions are particularly useful in problems involving periodic motion, such as pendulums. They can be defined in terms of the amplitude and elliptic modulus, linking them to the geometry of ellipses. The discussion highlights the need for a clearer definition of these functions for better understanding. Overall, Jacobi elliptic functions play a crucial role in various mathematical and physical applications.
Benjamin Goldstein
When doing a problem on a pendulum undergoing elliptical motion, I came across sn(z), which is apparently a "Jacobi Elliptic Function". When I looked into it further, I saw that these functions are essentially circular trigonometric functions but about an ellipse instead of a perfect circle. Can someone give me a more strict definition of each of the elliptic functions? Thanks.
 
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