Jacobi elliptic cn and dn

Last few days I was busy trying to understand some subtle points about Jacobi elliptic functions that I could not find clearly explained neither in Wikipedia nor in the literature that I was searching in the libraries and on internet. On internet I was able to find old treaties by the classics, like Legendre, as well as other old textbooks at archive.org. But nowhere I was able to find a clear explanation of how one can define in a simple way Jacobi elliptic functions am, sn, cn, dn for modulus k greater than 1. Finally, with the help stemming from useful comments, everything seems to fall in place.

In fact yesterday I wrote to prof. William A. Schwalm asking for some suggestions. He kindly wrote me back suggesting reading Chapter 4.3 of his monograph Lectures on Selected Topics in Mathematical Physics: Elliptic Functions and Elliptic Integrals (IOP Concise Physics) May 31, 2016. I did not have this book, so I bought it – the Kindle edition, instatly delivered to my Kindle. And yet, after perusing I could find what I was looking for. Will try to study deeper.
Continue reading “Jacobi elliptic cn and dn” »