Talk:Jacobi elliptic functions

message: Hello.  Sorry to remove good-faith additions, but I believe the French references will be of limited use to readers of an English wiki.  Best wishes, Robinh 21:28, 8 September 2007 (UTC)
replies: text: I don't see that that makes sense.  Lot's of people have studied French.  I think even more English speaking people have studied French than Spanish. Michael Hardy (talk) 21:09, 24 June 2010 (UTC)
thread_title: French references

message: It would be nice to have some graphical representation of at least some of these functions.  —Preceding unsigned comment added by 141.5.32.68 (talk) 10:08, 29 July 2010 (UTC)
thread_title:  Show some images? 

message: The introduction is very inaccurate and confusing. "corresponds to an arrow drawn from one corner of a rectangle to another" doesn't make any sense to me - what is the correspondence? An integral? If yes, over which function? And what is an arrow? I don't know that as a mathematical term, and the usual interpretation of an "arrow" doesn't make much sense to me in this context either. The introduction doesn't tell us either what the arguments of the elliptic functions are (the corners of the rectangle?)
The section "notation" says that an elliptic function takes two arguments, and the next section just talks about "sn u", which looks like one argument to the casual reader. --141.5.32.68 (talk) 16:36, 6 December 2010 (UTC)
thread_title:  Confusion in first three sections 

message: The phrase "Jacobi elliptic functions" is far more used than "Jacobi's elliptic functions", see these Google Scholar searches:  and ; as well as these Google Books searches:  and . So I moved the page to Jacobi elliptic functions. -- Crowsnest (talk) 18:02, 1 February 2011 (UTC)
thread_title:  Move to "Jacobi elliptic functions" 

message: Looks to me that the whole section "Definition in terms of trigonometry" is wrong. Could someone please double-check and delete or modify? The arc-length is computed as 
$$\int r(\theta) d\theta$$
but it should be
$$\int \sqrt{r(\theta)^2+r'(\theta)^2}d\theta.$$
This gives a more complicated integral.--> see edit next to diagram below. 37.250.2.216 (talk) 05:23, 11 June 2016 (UTC)
thread_title:  Mistakes 

message: To make the section better understandable, a diagram can say more than 1000 words.                                           
 
LWJdO (talk) 16:54, 29 July 2016 (UTC)
thread_title:  Diagram for Definition as trigonometry 

message: For x = cn(iu',m)/dn(iu',m), y=sn(iu',m)/dn(iu',m)
x^2 + (1-m) y^2 = 1
From Jacobi's imaginary transformation. Since
cn(iu',m) = 1/cn(u',1-m)  
sn(iu',m) = i sn(u',1-m)/cn(u',1-m)
dn(iu',m) = dn(u',1-m)/cn(u',1-m)
x = 1/dn(u',1-m)
y = i sn(u',1-m)/dn(u',1-m)
x^2 + (1-m) y^2  
= (1 - (1-m) sn(u',1-m)^2)/dn(u',1-m)^2 = 1
Q. E. D.  — Preceding unsigned comment added by Stephen William Wynn (talk • contribs) 15:19, 2 August 2016 (UTC)
thread_title:  Twin equation 

message: Consider the following text copied from the article:
"The Jacobian elliptic functions are then the unique doubly periodic, meromorphic functions satisfying the following three properties:
* There is a simple zero at the corner \mathrm p, and a simple pole at the corner \mathrm q.
* The complex number \mathrm p-\mathrm q is equal to half the period of the function \operatorname{pq} u; that is, the function \operatorname{pq} u is periodic in the direction \operatorname{pq}, with the period being 2(\mathrm p-\mathrm q). The function \operatorname{pq} u is also periodic in the other two directions \mathrm{pp}' and \mathrm{pq}', with periods such that \mathrm p-\mathrm p' and \mathrm p-\mathrm q' are quarter periods.
* If the function \operatorname{pq} u is expanded in terms of u at one of the corners, the leading term in the expansion has a coefficient of 1. In other words, the leading term of the expansion of \operatorname{pq} u at the corner \mathrm p is u; the leading term of the expansion at the corner \mathrm q is u^{-1}, and the leading term of an expansion at the other two corners is 1."
It is unsourced (the "uniqueness") and wrong (the third bullet in particular). For example, the residues of \operatorname{sn}(u,m) at the poles are \pm\tfrac{1}{\sqrt{m}}, so the coefficient of the leading term of the expansion at the pole is not always 1. A1E6 (talk) 14:02, 24 November 2021 (UTC)
thread_title:  "Abstract" definition of the Jacobi elliptic functions 

message: I'm not sure why the sections "Definition in terms of Jacobi theta functions" and "Comparison between sums and products" use the non-standard symbol \div. I was confused by this and needed to compare the formulas with https://functions.wolfram.com/EllipticFunctions/JacobiCN/27/02/08/ to confirm whether this really means just plain division. Per https://en.wikipedia.org/wiki/Division_sign:
"This usage, though widespread in some  countries, is not universal and the symbol has a different meaning in other countries. Its use to denote division is not recommended in the ISO 80000-2 standard for mathematical notation."
(Emphasis mine.) More concretely,
"The ISO 80000-2 standard for mathematical notation recommends only the solidus / or "fraction bar" for division, or the "colon" : for ratios; it says that the ÷ sign should not be used for division."
Please consider either replacing by the more appropriate /, or at least explaining the notation at its first usage. 2001:718:2:1801:0:1:E859:ABE (talk) 10:17, 9 February 2024 (UTC)
thread_title:  Div symbol 

message: I was looking for math article to translate into Spanish when I came across this article. There seems to be a lot of gibberish in this article, perhaps added in good faith by user Reformbenediktiner, but I tried to go back far enough to undo the edits and it goes back to 2022. I don't want to revert that far back but maybe someone with more complete knowledge of Jacobi functions can make a more informed decision. I'm not trying to start a flame war, but I recommend undoing revisions at least through March 2024, almost definitely through 28 May 2023, and  possibly all the way through the first 2022 revisions by this user. I definitely cannot integrate more recent revisions by other users with reverting to such an early date. JuanTutors (talk) 00:10, 26 March 2024 (UTC)
replies: text: Yes, it would be great to clean this article back up. I don't feel competent to do it. Feel free to explicitly ping other editors who have worked on this or go ask for help at WT:WPM. –jacobolus (t) 00:55, 26 March 2024 (UTC)
replies: text:  I have restored this version, from a year ago.  I cannot say whether all of the edits in the interim were necessarily bad, per se, but a lot of dubious stuff was added, and the notation was completely changed without discussion.  Most other intervening edits seemed minor, so the collateral damage of this revert minimal, but I may have missed something important.  (It was tempting to revert even deeper, because the same editor had added some other stuff, but instead I removed a section that seemed very offtopic here.)  Tito Omburo (talk) 14:32, 7 April 2024 (UTC)
thread_title:  Gibberish in article