Talk:Weierstrass elliptic function

message: The homogenity relation doesn't seem to work for all c since cτ may not remain in the upper half plane. I don't quite understand how this relation can serve to define doubly periodic functions with arbitrary period pairs.
:It would probably be better to choose parameter Λ = periodic lattice initially, rather than τ. Taking the reciprocal of τ would fix up the imaginary part, and that's taking the basis for periods in the other order. That in fact is just a special case of the PSL (2,Z) action that is implicit in choice of general basis, and which means τ can be taken to be in the usual fundamental domain within the upper half plane. But I'd agree this is tough on the reader - does two steps at once. Charles Matthews 19:31, 10 Feb 2004 (UTC)
replies: text: \mathcal{P}(z;\tau) =\frac{1}{z^2} + \sum_{n^2+m^2 \ne 0}{1 \over (z-n-m\tau)^2} - {1 \over (n+m\tau)^2}
This correction and some of the other comments are good, but it seems to me in many ways the article has been messed up and dumbed down from the way I left it. Why drag in the old-fashioned half-period formulation, and then say things inconsistent with it? What was wrong with sticking to the modular formulation? 
A lot of stuff has been replaced with a regurgitation of old-fashioned points of view and formulas which do not related to the article on theta functions. Gene Ward Smith 07:36, 20 July 2005 (UTC)

text: Hi, Welcome back to Wikipedia (as I notice you've been gone a long time). I've been editing the article on and off; its possible that some of what you are complaining about are edits I've made, for which I'm sorry. As to "old-fashioned points of view", I'm not sufficiently advanced on the topic to be able to tell the difference between old and new.  I know I've worked "from the literature"; if I tripped across a relation that seemed useful, I'd add it to the article.  I admit that this is not a very elegantly structured article, which has bugged me, but I haven't had any vision to make any overhauls, with the exception of modular discriminant, which I wanted to make into its own stand-alone article. linas 14:34, 20 July 2005 (UTC)
replies: text: Oh, and as to "dumbed down", be aware that there has been ooodles of screaming about "too complicated" in many other math articles. A policy I've tried to hew to, is that, for an article like this, an average college student with a good grounding in calculus (or an average professor with absolutely no prior experience at all with elliptic/modular functions) should be able to read at least half-way through the article before getting mired.  Thus, Charles Matthews definitions regarding a field C[P,P'] that is a ring of polynomials over C is good, but should occur somewhere other than the beginning of the article, as it would hopelessly throw the beginners for a loop.  The current article seems readable; if its lacking a more modern or more formal or a more high-brow definition, it should be added (but I don't know what that might be). Hope I'm not sounding too bombastic here.  linas 14:51, 20 July 2005 (UTC)
thread_title:  Early article discussion 

message: In the section about the e_i, the \omega_i change their meaning from periods to half-periods without much warning, it is confusing.--Bernard 22:27, 6 August 2006 (UTC)
replies: text: My vote is for periods, it seems more natural to me, but I have no textbook to compare with. --Bernard 21:07, 7 August 2006 (UTC)
replies: text: I would be very happy to have the omegas as periods everywhere, which is the convention I was brought up on (and my doctorate was in this area). Charles Matthews 21:37, 7 August 2006 (UTC)
thread_title:  Periods or half-periods? 

message: can someone please explain what a pe-function is supposed to be?  I've seen this thing called p-function zillions of times, but never pe-function.--345Kai 03:22, 5 April 2007 (UTC)
thread_title:  Pe-function?? Peh-function?? 

message: As my daughter used to say.
Not to be "down and dumb" but "what's it for" ? ( cool graphic on unit disk)
Does this have applications (used to represent xxxx )in  electricity, chemistry, structural analysis, natural phenomenon. DG12 (talk) 20:31, 10 November 2011 (UTC)
replies: text: in fact, elliptic functions have plenty of applications (in particular, to electricity, starting from the classics), but this is not the place to discuss them (see WP:Talk page guidelines). Sasha (talk) 01:48, 11 November 2011 (UTC)
thread_title:  What about me, the end user

message: The section on the  modular discriminant  \Delta  is not consistant as currently written. The section defines the discriminant in terms of the g_2  and g_3 coefficients, which are in turn defined  in terms of general periods. Thus we have 
\Delta(\omega_1,\omega_2).   The discriminant section, however,   claims that \Delta = (2\pi)^{12} \eta^{24}.  This is not correct. It  is \Delta(1, \tau) that is equal to (2 \pi)^{12} \eta^{24}.  The power \eta^{24} is a modular invariant. The discriminant is a modular form of weight 12.
I don't want to meddle with the writing in case I make things worse. A regular page maintainer should do it.
Mike Stone (talk) 14:23, 19 April 2012 (UTC)
thread_title:  An inconsistancy. 

message: The definition of modular discriminant as given now is incostistent with the convention used at Modular form#The modular discriminant and Ramanujan tau function. I think the convention used in those two pages (without the (2\pi)^{12} factor) is more common, however both of them appear in literature, and the convention with the factor used here arguably makes more sense in the context of elliptic functions. However this inconstistency should be resolved somehow, and mention of the existence of two different conventions in literature should be added (perhaps both here and at Modular form#The modular discriminant). But I don't wanna make this decision unilaterally and would appreciate some feedback from regular maintainers of this page. GreenKeeper17 (talk) 18:53, 6 April 2017 (UTC)
thread_title:  Two conventions for modular discriminant 

message: What's about the Weierstrass Constant 0.474949...? 46.115.82.168 (talk) 14:40, 31 May 2013 (UTC)
thread_title:  Weierstrass Constant 

message: In the section "Invariants", expressions for the two independent quantities g_2 and g_3 are given in terms of \tau and \omega_1. However, in the section "The constants e_1, e_2 and e_3", the dependence on \omega_1 is dropped.  There should be two independent parameters describing e_1, e_2 and e_3 (because e_1+e_2+e_3=0), but there is only \tau.  I can see two possible resolutions.  Either explicitly state that \omega_1=1 and \omega_2=\tau, or even better, include a second parameter (such as \omega_1) so that all cases are covered.
Yzarc314 (talk) 14:06, 25 July 2017 (UTC)
thread_title:  Missing parameter in section "The constants <math>e_1, e_2</math> and <math>e_3</math>" 

message: A pointer: there was discussion about the symbol ℘ in Talk:Weierstrass p#Cleanup, now a redirect to this page. -- Teika kazura (talk) 00:06, 18 September 2018 (UTC)
thread_title:  Past discussion about the symbol ℘ 

message: " if c is any non-zero complex number,
{\displaystyle \wp (cz;c\tau )=\wp (z;\tau )/c^{2}} "
This is surely wrong, it is inconsistent with a similar rule where in the second argument the whole lattice is multiplied by c (not just the second basis element).Createangelos (talk) 11:28, 27 October 2018 (UTC)
thread_title:  General Theory typo 

message: Instead of listing three concepts within one paragraph, split them out into a list. This lets the physical structure of the text better match the conceptual structure.
Currently:
The Weierstrass elliptic function can be defined in three closely related ways, ...<snip>..., for fixed z the Weierstrass functions become modular functions of τ.
I suggest:
The Weierstrass elliptic function can be defined in three closely related ways, each of which possesses certain advantages: 
    1) As a function of a complex variable z and a lattice Λ in the complex plane. 
    2) In terms of z and two complex numbers ω1 and ω2 defining a pair of generators, or periods, for the lattice.
    3) In terms of z and a modulus τ in the upper half-plane. This is related to the previous definition by τ = ω2/ω1, which by the conventional choice on the pair of periods is in the upper half-plane. Using this approach, for fixed z, the Weierstrass functions become modular functions of τ.
Michael McGinnis (talk) 02:24, 31 January 2020 (UTC)
thread_title:  Suggestion: Split paragraph into Short paragraph and short list 

message: then please let someone else edit Wikipedia.
Case in point:
" Since the square of the derivative of Weierstrass' elliptic function equals the above cubic polynomial of the function's value, \wp'\left(\frac{\omega_i}{2}\right)^2=\wp'\left(\frac{\omega_i}{2}\right)=0 for i=1,2,3."
The "above cubic"?  The "above cubic"?
I looked all over and there were so many third powers that it is ridiculous to expect the reader to be able to figure out what the author was thinking.
If you're going to refer to an equation or anything else that a) is nowhere near your reference text and b) is not labeled at all ... then please: say what you mean.
Thanks.2600:1700:E1C0:F340:4CA2:1162:525:8896 (talk) 23:47, 25 September 2019 (UTC)
thread_title:  Suggestion: If you are too tired or low-energy or pressed for time ... 

message: The expresions for g_2 and g_3 in this article state that they have a q-expansion that has only even powers, which is not true. 128.41.61.181 (talk) 17:23, 9 June 2023 (UTC)
thread_title:  Wrong expressions for g_2 and g_3