Jacobi Elliptic Functions and Integrals

Click For Summary

Discussion Overview

The discussion revolves around Jacobi Elliptic functions and their geometric interpretations, particularly in relation to ellipses and their connection to circular trigonometric functions. Participants seek resources and references that provide intuitive explanations and visual representations of these concepts.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant requests references that intuitively explain the geometric interpretation of Jacobi Elliptic functions in relation to ellipses and their generalization of circular trigonometric functions.
  • Another participant shares a web article that discusses the correspondence between points on an ellipse and a circle, suggesting it may be of interest.
  • A third participant expresses interest in finding resources on hyperbolic functions and their parallels to trigonometric functions, while also inquiring about a specific article that appears to be unavailable.
  • A different participant recommends the Digital Library of Mathematical Functions as a potential resource for information on special functions, noting it may not cover everything but could be useful.

Areas of Agreement / Disagreement

Participants are generally seeking resources and information, but there is no consensus on specific references or the completeness of the available resources. The discussion remains open-ended with various inquiries and suggestions.

Contextual Notes

Some participants express uncertainty about the availability of specific articles and resources, indicating limitations in access to certain materials.

Who May Find This Useful

Readers interested in Jacobi Elliptic functions, their geometric interpretations, and connections to trigonometric and hyperbolic functions may find this discussion valuable.

bamajon1974
Messages
22
Reaction score
5
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!
 
Mathematics news on Phys.org
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
 
  • Like
Likes   Reactions: DrClaude and BvU

Similar threads

  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 11 ·
Replies
11
Views
2K
  • · Replies 11 ·
Replies
11
Views
3K