Jacobi Elliptic Functions and Integrals

[bamajon1974]

Are there any useful references or resources that intuitively show how Jacobi Elliptic functions [sn, cn, dn, etc] are geometrically interpreted from properties of ellipses? And how the Jacobi Elliptic functions and integrals can be shown to be generalizations of circular trig functions? Thanks!

 

[anuttarasammyak]

I found the web article with skech,
http://arkadiusz-jadczyk.eu/blog/2017/01/jacobi-elliptic-functions-definition-trigonometry/
may be of your interest.
We correspond a point on the ellipse to the point on the circle within.

 

[bamajon1974]

This article helps. I will check it out. Do you know of a corresponding website for hyperbolic functions and their parallel trig functions as well?

Do you happen to have the article referenced in the website? The pdf file doesn't seem to exist anymore.
https://und.edu/error-dept-404.html...ct/schwalm/maa_presentation_10-02/handout.pdf

Thanks!

 

[jasonRF]

The first place I always look for info on special functions is the Digital Library of Mathematical Functions
https://dlmf.nist.gov/
It might not have everything you are looking for, but it does have some of it. Have you looked there?

Jason