User talk:A1E6

Welcome to my Talk page! Please ignore the messages from 2019–2021. I didn't know much about the Wikipedia project back then.

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15:00, 14 February 2019 (UTC)

\operatorname

Just a heads up, but the use of \operatorname for functions like $\Gamma (z),\,\zeta (z),$ etc. is generally inappropriate. –Deacon Vorbis (carbon • videos) 23:55, 24 February 2019 (UTC)

I don't think that

\Gamma (n)\Gamma \left({\frac {n}{2}}\right)

is better than

\Gamma (n)\operatorname {\Gamma } \left({\frac {n}{2}}\right)

. As you can see, \operatorname fixes inappropriate spacing in the case of functions with fractional arguments. \sin, \cos and so on are exceptions. –A1E6

Please indent your replies and keep conversations in one location; see Help:Talk for more details. It's a very small difference, and fiddling with spacing should only be done when really necessary. Moreover, this will leave functions named with Latin alphabet letters inconsistent (e.g.

f(x)f\left({\frac {x}{2}}\right),

because it's not possible to use \operatorname without making the f set in roman. Plus, doing it like this, the spacing is now wrong on the left instead. Also, testing this on a normal LaTeX distribution, using \opertorname doesn't produce the same effect. So this is just exploiting a weird quirk in the Texvc engine that Mediawiki uses in order to produce spacing that you happen to think is slightly better, but only for greek-letter function names. That's not a good enough reason to make such changes.

{\begin{aligned}&\left.{\begin{array}{l}n\Gamma (n)\\[4pt]n\operatorname {\Gamma } (n)\end{array}}\right\}\longleftarrow {\text{These conspicuously differ from each other typographically.}}\\[6pt]&n\cos(n)\end{aligned}}

It does appear that the spacing is the same as the standard spacing with \cos, \log, \exp, etc. only when \operatorname{} is used. That does not surprise me. Michael Hardy (talk) 16:26, 25 February 2019 (UTC)

I would not call \cos, \log, \det, \max etc. "exceptions"; rather I would say they are already operatornames. The spacing to their left and right depends on the context, as with \operatorname{}. Michael Hardy (talk) 16:27, 25 February 2019 (UTC)

Thank you very much for an explanation. A1E6 (talk) 17:37, 25 February 2019 (UTC)

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July 2020

Hello, I'm DVdm. I noticed that you made a change to an article, Generalized continued fraction, but you didn't provide a source. I’ve removed it for now, but if you’d like to include a citation to a reliable source and re-add it, please do so! If you think I made a mistake, or if you have any questions, you can leave me a message on my talk page. Thanks. DVdm (talk) 18:37, 13 July 2020 (UTC)

Inverse trig functions

You reverted my change of 2020-09-03 on 2020-09-05. I believe it was valid. I now also have several other changes to the Logarithmic Forms that I believe make them valid everywhere for principal values of the functions, not just on the complement of the branch cuts. I am opening a section called Complex logarithmic forms in the Talk for the article where we can discuss all this if you are interested. Rickhev1 (talk) 18:29, 8 September 2020 (UTC)

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Sources please

Please do not add or change content, as you did at Sine, without citing a reliable source. Please review the guidelines at Wikipedia:Citing sources and take this opportunity to add references to the article. Thank you. - DVdm (talk) 15:49, 1 March 2021 (UTC)

Note, see also wp:NOR and wp:CALC. Cheers. - DVdm (talk) 15:50, 1 March 2021 (UTC)

I consider my edit to be an improvement for Wikipedia. In my opinion, it might be helpful and interesting for many Wikipedians. But here, bringing up the "no unsourced content" rule seems a bit off, considering that there are no sources at all in the "Arc length" section, yet the stuff still stays there (most importantly the expression of the arc length in terms of the gamma function) and considering that the proof I provided can be easily followed—the proof is in the spirit of many other Wikipedia proofs which are unsourced and stay on Wikipedia.

Unsourced content is not an invitation for more unsourced content, but I do not find strictly obeying the "no unsourced content" rule to be beneficial for anyone in the case of my edit. One could say that unsourced content has still its place on Wikipedia because of how old the edits are and because the community consensus is that they are fine.

In my view, the "no unsourced content" rule is less relevant for mathematics than for any other field of study which has its community on Wikipedia (given that proofs of the theorems are provided). Maybe, if you gave my edit some time, it would still be there, just as the expression in terms of the gamma function mentioned above. Would this make my edit "accepted by community", among dozens of other accepted unsourced contributions?

Imagine how poor would **mathematics** on Wikipedia be if everyone was constantly reverting every contribution that involves no source. Where would such Wikipedia be today?

Also, I do not want to be rude, but if I am not mistaken, in your edit summary, you called the needed citation "inlikely" (I think you meant unlikely), but at the same time, you want me to "take this opportunity to add references to the article"—this is rather contradictory and if anyone is possibly willing to add the references in the future, calling them "unlikely" hardly motivates the editors to do so.

However, if you just don't like my edit or edits of similar nature, I respect that. A1E6 (talk) 02:56, 3 March 2021 (UTC)

It's not a question of liking. Wikipedia needs sources (1) for verifiabiliy, and (2) to make sure that added content is worthwile to be included. If we discover new mathematical truths and the world doesn' care, then Wikipedia cannot take it on board. After all, by design, it's an encyclopedia, not a textbook. My apologies for the addition of "unlikely", and for the typo

. - DVdm (talk) 10:44, 3 March 2021 (UTC)

"If we discover new mathematical truths and the world doesn't care..."

I think that "If we discover new mathematical truths and the world doesn't **know**..." suits your thought much better. The words have very different meanings, otherwise I wouldn't be pointing this out.

For the sake of clarity, my edit didn't resemble a textbook at all. There were no instructions, no leading questions and no systematic problem solutions. The way the information was presented had a 100 % "state-the-facts" tone. So I quite don't understand why you're referring me to WP:NOTTEXTBOOK.

My aim was just to expand the poor and unsourced "Arc length" section. In general, adding unsourced content is not always a good idea, but given the circumstances in the "Arc length" section, I used the WP:IAR as I thought that the edit was definitively improving the section (and I still do, but if you're against it, I am not able to do anything with it unless I have the citations).

I do not want to encourage you to delete anything, but from my view, your actions would be understandable if they included the deletion of the whole unsourced "Arc length" section, otherwise not. Yes, I know, "community consensus", but nothing was preventing you from waiting and possibly seeing how my edit becomes a part of unsourced Wikipedia which is accepted by the whole community and makes the mathematics part of Wikipedia a better place.

Would this be more helpful and more useful for the community than me waiting for someone to publish the result in a journal or some book? I think it would. In case of any doubts (this probably wouldn't have happened, the result is easily verifiable, by the way, but that's not important here), any problems could have been resolved in the article's Talk page.

That is just my opinion, though. A1E6 (talk) 13:53, 3 March 2021 (UTC)

If you think the whole unsourced "Arc length" section should be deleted, then, given the fact that it has been sitting there for quite some time, the place to discuss this is the article talk page. Perhaps it is sourced, but not "inline". Perhaps there is no source, but there was some de-facto consensus to keep it anyway. For new content, there is the wp:BURDEN upon the provider to get the sources. See also User talk:DVdm#Edit reverted. - DVdm (talk) 12:46, 4 March 2021 (UTC)

For the record, I don't want the section to be deleted. I thought that you could have deleted it a long time ago though, before it even "reached" consensus.

I don't know why you're referring me to WP:PROVEIT when I actually provided a proof. After I provided it, the verifiability was not likely to be challenged. And I'm sorry but, except for the case of creating whole new articles, I can't seem to find the "content must be **worth** mentioning" rule (which you discussed on your talk page with someone) anywhere on Wikipedia policy pages – could you please refer me there, if possible?

Nevertheless, I think that a compromise would be more useful than deleting it all for everyone viewing the article. The readers could make use of the facts presented in my edit, while being alerted by the "Citation needed" tag, as in the case of Anita5192's edit.

With the "Citation needed" tag, it was possible that some editor would actually find the citation and add it there, but now that you've deleted it all, it's not possible for them (unless they're browsing diffs, which is much less probable than just viewing the article). A1E6 (talk) 23:22, 7 March 2021 (UTC)

See WP:DUE. Also note that wp:BURDEN (aka wp:PROVIT) is about providing sources, not about proving content: The burden to demonstrate verifiability lies with the editor who adds or restores material. (bolding form original, underlining mine). I can prove that 464646446446 + 323232323233 = 787878769679. Shall I mention that (with my proof) in article Addition? Try to imagine what would happen to Wikipedia if we let go of wp:BURDEN. - DVdm (talk) 10:40, 8 March 2021 (UTC)

464646446446 + 323232323233 is a routine calculation (WP:CALC) and hence is not comparable to my edit. I just want to say that, if anything, leaving the "Citation needed" tag would be more appropriate than deleting it all (see also the above message). A1E6 (talk) 11:12, 8 March 2021 (UTC)

Allright, I can prove that

\int _{1}^{e}\ln {\frac {1}{x}}dx=-1.

We take it?

In my experience a {{cn}} tag for the kind of content that you added would be sitting there for years. - DVdm (talk) 12:12, 8 March 2021 (UTC)

There you go

. - DVdm (talk) 09:28, 11 March 2021 (UTC)

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Dimension maximizing the volume of a fixed-radius ball

Thank you. For many years I've been thinking that I am (almost) alone. Almost always. Guswen (talk) 17:46, 23 November 2021 (UTC)

No problem. A1E6 (talk) 17:48, 23 November 2021 (UTC)

Simple algebraic expression

Dear A1E6,

I have been attempting to introduce a simple and straightforward simplification of the black hole surface gravity. Schwarzschild radius is $R_{BH}={\frac {2GM_{BH}}{c^{2}}}$ . Hence $M_{BH}={\frac {R_{BH}c^{2}}{2G}}$ . Thus a black hole surface gravity is $g_{BH}={\frac {GM_{BH}}{R_{BH}^{2}}}={\frac {G}{R_{BH}^{2}}}{\frac {R_{BH}c^{2}}{2G}}={\frac {c^{2}}{2R_{BH}}}={\frac {c^{2}}{D_{BH}}}$ . This form is simpler as it depends only on D, but the "resistance of the matter" is similar to that that we experienced in our struggle to maintain the unit n-ball picture in the Volume of an n-ball last November . I am not an experienced Wikipedian, so I simply don't know what should I do. I will appreciate, and in advance I thank you for an advice. Guswen (talk) 08:52, 8 March 2022 (UTC)

Hi Guswen,

The "resistance of the matter" is quite different from the unit n-ball – since the unit n-ball stuff can be backed by sources (but I'm not sure if your derivation can). For what it's worth, I think that your derivation is too simple to be considered "research" (or original research, for that matter), given that you combined two known facts. However, it's understandable that someone, perhaps in the field of physics, can have a different opinion. There can also be notability issues, meaning that even if the derivation is straightforward, it has to be in some reputable sources.

Tarl N. was not satisfied with your contribution, referring to WP:SYNTH. Perhaps you could use WP:NOTJUSTANYSYNTH, in particular: SYNTH is original research by synthesis, not synthesis per se. Maybe there's a good chance that someone came up with the same thing as you did – in that case, my advice would be to search for sources. A1E6 (talk) 15:04, 8 March 2022 (UTC)

For what it's worth, see discussions on article talk page and user talk page. My main objection at this point is mainly "what's the point?". It's not something that has been found meaningful elsewhere (at least not enough to publish), and it's not relevant to the subject of the article, Surface gravity in general. It's something specific to black holes, and an obscure factoid which doesn't seem to have any particular relevance.

I have a lot of objections with how my interaction with Guswen has gone, among other things that they like to forum shop. I've informed the editor what the dispute resolution mechanisms are, and they have either been roundly ignored or misused - they tried 3O and neglected to notify the other parties in the dispute. Didn't matter, the matter was rapidly rejected from consideration. This last instance where they decided that three months after a discussion ended, to simply re-introduce the changes with a comment to the effect of you didn't win, I'm doing it anyway, I found particularly irritating. Regards, Tarl N. (discuss) 17:32, 8 March 2022 (UTC)

Lemniscate constant formula

Hi, you have improved the Lemniscate elliptic functions page a whole lot and you have my gratitude for it, I don't understand much but there is aformula that catched my attention which you added in February $\varpi ={\frac {\pi }{\sqrt {2}}}\left(\sum _{n\in \mathbb {Z} }e^{-\pi n^{2}}\right)^{2}={\sqrt {2}}\pi e^{-\pi /6}\left(\sum _{n\in \mathbb {Z} }(-1)^{n}e^{-\pi (3n^{2}-n)}\right)^{2}.$ later you cited a reference which contains the first equality but I think it doesn't contains the second so I would like to ask you how is done (or a reference), thanks in advance and best regards Dabed (talk) 21:30, 11 June 2022 (UTC)

Hi. From Ramanujan's Notebooks Part V by Bruce C. Berndt (p. 326) we have

\sum _{n\in \mathbb {Z} }(-1)^{n}e^{-\pi (3n^{2}-n)}={\frac {2^{-1/2}e^{\pi /12}\pi ^{1/4}}{\Gamma (3/4)}},

\sum _{n\in \mathbb {Z} }(-1)^{n}e^{-\pi (3n^{2}-n)/2}={\frac {2^{-3/8}e^{\pi /24}\pi ^{1/4}}{\Gamma (3/4)}}.

This is equivalent to the desired result since

\Gamma (3/4)=2^{-1/4}\pi ^{3/4}\varpi ^{-1/2}

. A similar result appears in The Lemniscate Constants by John Todd (p. 18, Theorem 18). A1E6 (talk) 21:51, 16 June 2022 (UTC)

Found the second reference but not the first one nevertheless as it is the relevant one added it in the article, hope to get the chance to eventually came across the Ramanujan notebooks. Thanks a lot and best regards. Dabed (talk) 20:20, 17 June 2022 (UTC)

Volume of an n-ball

Dear A1E6,

My recurrence relation without $\pi$ was eventually published^[1], so I have added it for this article. Maybe some other researcher discovers, on this basis, fractional forms of this sequence, for example (?). However, my edit was again reverted by User:David_Eppstein as "Undo the return of the ridiculous negative-dimensional crankery". Why? Guswen (talk) 13:44, 26 June 2022 (UTC)

David Eppstein uses the word "crankery" quite frequently. But you still can't add the article yourself (this applies to your associates as well), as self-promotion is prohibited on Wikipedia. A1E6 (talk) 15:24, 26 June 2022 (UTC)

Thank you. I didn't know about this policy. So I will wait until someone else adds it. Guswen (talk) 15:35, 26 June 2022 (UTC)

Predatory journals are prohibited on Wikipedia as well, see MDPI#Controversies. A1E6 (talk) 15:37, 26 June 2022 (UTC)

But MDPI Mathematics is not considered predatory by the National Publication Committee of Norway, for example. Furthermore, this recurrence relation is easily confirmableed by anyone armed with a pencil and a sheet of paper.Guswen (talk) 18:15, 26 June 2022 (UTC)

References

[1]
Łukaszyk, Szymon (2022-06-24), Licata, Ignazio; Schneider, Carsten (eds.), Novel Recurrence Relations for Volumes and Surfaces of n-Balls, Regular n-Simplices, and n-Orthoplices in Real Dimensions, MDPI Mathematics, doi:10.3390/math10132212, retrieved 2022-06-24{{citation}}: CS1 maint: unflagged free DOI (link)

Nome (mathematics)

Now I provided even many essay sources that contain the hyperbolic lemniscate cotangent. I know the page Bring radical#The Hermite–Kronecker–Brioschi characterization already and I researched all the formulas I entered into the nome article very accurate. I even derived and established these formulas very detailled. Therefore I hope that you will not erase these very important formulas ever again. These formulas are exactly correct and they indeed belong to the nome article. So leave these formulas inside this Wikipedia article! The sources support the formulas. And please do me even a further favour! Please read the German Wikipedia article https://de.wikipedia.org/wiki/Bringsches_Radikal very carefully! In this article the Bring radical is defined with a positive first derivative and therefore negative to the definition some other sources make. But all these formulas in that article according to the definition made in this article are correct. And this German article with the name "Bringsches Radikal" describes everything even extremely accurate. There are also all these essays that bring forth all these formulas that are standing in this German Wikipedia article. Especially the essay of Charles Hermite and the essays of the mathematicians Young and Runge and all these authors of mathematical essays explain the thing with the modulus and the fifth root radical combinations of the elliptic key and the transformation to the Rogers-Ramanujan continued fractions and everything else very extensively. And all of these definitions of the hyperbolic lemniscate functions I gave in the nome article can also be found in many sources. For this purpose please read the German Wikipedia article Hyperbolisch lemniskatischer Sinus on that page: https://de.wikipedia.org/wiki/Hyperbolisch_lemniskatischer_Sinus I wish you the best understanding and have a nice time!

Lion Emil Jann Fiedler also known as "Reformbenediktiner" Reformbenediktiner (talk) 08:34, 4 July 2022 (UTC)

@Reformbenediktiner: Can you work out the general case

x^{5}+x=w

where

w

is an arbitrary complex number and express all five complex roots (counted with multiplicity)? The section Bring radical#The Hermite–Kronecker–Brioschi characterization does that, but it is missing in the Nome (mathematics) article. A1E6 (talk) 12:38, 4 July 2022 (UTC)

The other four roots, the imaginary roots in this case, can be constructed by putting the imaginary fifth roots of one as a factor before the fifth root of the nome value. Then it looks like this:

x_{{\text{Im}}1}={\frac {S{\bigl \langle }q_{{\text{Im}}1}{\bigr \rangle }^{2}-R{\bigl \langle }q_{{\text{Im}}1}^{2}{\bigr \rangle }}{S{\bigl \langle }q_{{\text{Im}}1}{\bigr \rangle }^{2}}}\times

\times {\frac {1-R{\bigl \langle }q_{{\text{Im}}1}^{2}{\bigr \rangle }\,S{\bigl \langle }q_{{\text{Im}}1}{\bigr \rangle }}{R{\bigl \langle }q_{{\text{Im}}1}^{2}{\bigr \rangle }^{2}}}\times

\times {\frac {\vartheta _{00}{\bigl \langle }q_{{\text{Im}}1}^{5}{\bigr \rangle }\,\vartheta _{00}{\bigl \langle }q_{{\text{Im}}1}^{1/5}{\bigr \rangle }^{2}-5\,\vartheta _{00}{\bigl \langle }q_{{\text{Im}}1}^{5}{\bigr \rangle }^{3}}{2{\sqrt[{4}]{20}}\,{\text{sl}}[{\tfrac {1}{2}}{\sqrt {2}}\,{\text{aclh}}({\tfrac {5}{4}}{\sqrt[{4}]{5}}\,w)]\,\vartheta _{00}{\bigl \langle }q_{{\text{Im}}1}{\bigr \rangle }^{3}}}

q_{{\text{Im}}1}={\bigl [}{\tfrac {1}{4}}({\sqrt {5}}-1)+{\tfrac {1}{4}}{\sqrt {10+2{\sqrt {5}}}}\,i{\bigr ]}q\{{\text{ctlh}}[{\tfrac {1}{2}}{\text{aclh}}({\tfrac {5}{4}}{\sqrt[{4}]{5}}\,w)]^{2}\}

But this should not be entered into this formula alone unless the Rogers-Ramanujan R and S continued fractions are replaced by these theta function therms appearing in the definition formulas for R and S:

R(y)=\tan {\biggl \langle }{\frac {1}{2}}\operatorname {arccot} {\biggl \{}{\frac {\vartheta _{01}(y^{1/5})[5\,\vartheta _{01}(y^{5})^{2}-\vartheta _{01}(y)^{2}]}{2\,\vartheta _{01}(y^{5})[\vartheta _{01}(y)^{2}-\vartheta _{01}(y^{1/5})^{2}]}}+{\frac {1}{2}}{\biggr \}}{\biggr \rangle }

S(y)=\tan {\biggl \langle }{\frac {1}{2}}\operatorname {arccot} {\biggl \{}{\frac {\vartheta _{00}(y^{1/5})[5\,\vartheta _{00}(y^{5})^{2}-\vartheta _{00}(y)^{2}]}{2\,\vartheta _{00}(y^{5})[\vartheta _{00}(y^{1/5})^{2}-\vartheta _{00}(y)^{2}]}}-{\frac {1}{2}}{\biggr \}}{\biggr \rangle }

Then this should give the imaginary four solutions of this Bring-Jerrard quintic equation. This must be the way to produce the other solutions of this quintic equation. Hopefully you can understand this explanation. And I really hope, that I could help you with that information. I see one thing that makes me a bit unsecure. Originally the tangent of the half of the arc cotangent as it is shown in the R and S definition formulas could lead to two different values for imaginary abscissa values because it contains a square root. Unfortunately I am not such a big expert in imaginary mathematics. But I nevertheless hope that my entry at your page was at least a bit helpful. But I swear to you, that I know exactly that the formula I have entered in the nome article is definitely totally correct. And yes, I worked these formulas out by using exactly these essay sourced I have listed at the end of the nome article. And I even made many experiments by myself with this formula and this formula always works for the real solutions. What w value ever I put in, the formula always gives the right solution. I gave the example for w = 3 in the nome article and the formula really produces this value 1.132997565885... of the solution. But I did what I could do and I really gave my very best. I put a lot of effort into the enlargement of this elliptic nome Wikipedia article. So I really hope that no formula of this article will be erased. I hope that every single formula will stay inside very well preserved. My work was not just a theory finding, it really was thorough research in the literature and I only used what was well documented. Hopefully nobody will delete my formulas. I researched all the formulas about the elliptic nome extremely thoroughly and very accurately. I checked the values in the value list of the nome accurately and carefully for correctness. And then I entered all these formulas. And the many infinite sum and product identities I could find out by making a lot of calculations, computations and experiments. I also wrote down the nome formulas on many of my papers and calculated also on these papers. And so I found everything out. And I have this big wish, that every single mathematically interested reader of the elliptic Wikipedia articles is informed in a very brillant way. The readers shall get the best formula knowledge they can ever get. This is really my great wish I totally want to fulfill. Now I want to ask you one thing. Is my behaviour acceptable? Or did I go to far? Am I allowed to behave that way and to enter one formula after the other one into all these mathematical Wikipedia articles? I really want to share my knowledge with the other mathematically interested humans in the world. I never did study mathematics. But it is my big hobby. And I love mathematics very much. Mathematics is my favourite subject since I was a child. And I also dream a lot of mathematics. The same thing I made in my childhood. I am even interested a little bit more in scientific subjects than in humans. This has something to do with the fact, that I have Asperger's syndrome in myself. Asperger's syndrome is a special kind of autism and I really have it. I belong to the one percent of humanity that has this mental aptitude. But I am proud of it. And hopefully you will perceive my interventions in the pages of Wikipedia with positive feelings. I see in writing these Wikipedia articles a great commission or a great task, which was entrusted to me by the almighty creator of the world. And I want to fulfill this big plan. For me, writing the Wikipedia articles is sometimes even like a great passion or maybe even a vehement drug that I can not resist. But it is always a big joy for me and it makes me lucky. Now I explained you very much and gave you a big amount of information. I wish you a very good time and a lot of success. Yours faithfully and sincerely! Lion Fiedler also known as Reformbenediktiner Reformbenediktiner (talk) 21:24, 4 July 2022 (UTC)

@Reformbenediktiner: Yes, I think you went too far. You provided some references, but a significant amount of original research is needed to arrive at your result (original research is prohibited on Wikipedia, per WP:OR) and your calculations extend far beyond WP:CALC. I'm not going to remove your contribution again, but note that anyone willing to remove it in the future has the right to do so. A1E6 (talk) 01:47, 5 July 2022 (UTC)

Alright! I will be much more careful from now on. And I watched out, that I do not enter results of original research. I really watched out, so that I do not produce any complications. I made some entries into the article Jacobi elliptic functions. This time I behaved the right way. I did not make original research but I really used the Literature. The sequence and its correlations were found out already by many mathematicians I quotated and citated in the Literature list at the end of this article and I was careful. And the fraction formulas for K were also found out by mathematicians. This time I only formulated the formulas more accurate. Hopefully I did everything right this time. I do not want to provocate and I do not want to cause trouble. I just want to help and to inform the mathematically interested readers. But I want to get one special answer on one important question. How exactly can I notice if I did everything correct? How can I get secure, that I did not make an original research by entering formulas in Wikipedia articles? Making this difference is sometimes a bit difficult for me. Maybe I should wait an intermediate time until I produce the next formulas in the Wikipedia articles. Perhaps I should wait until the other Wikipedia users will read my formulas accurately and controlled everything and checked if everything is acceptable. Yes, I think that the next time I will enter formulas in Wikipedia articles will be in a few months. But then I definitely start to add good formulas into the Wikipedia articles again. I feel sorry, that I confused you and other Wikipedia users. I just wanted to give my best. I will promise that I avoid this mistake named original research and I focus a lot more on the correctness of the literature. Maybe I should really wait for a longer time with all my productions in the English Wikipedia articles. The users on the German Wikipedia articles could get along with my formulas in an intermediate way. Maybe I should tell you, that my Wikipedia account with the name Reformbenediktiner indeed belongs to the German Wikipedia. I have been working for the German Wikipedia pages for many months and even years. I dealt with many topics in the Wikipedia articles already. But my focus is located on the mathematical Wikipedia articles. Have a nice time!

Lion Emil Jann Fiedler — Preceding unsigned comment added by Reformbenediktiner (talk • contribs) 14:20, 6 July 2022 (UTC)

@Reformbenediktiner: I've already noticed that a large part of your contributions to German Wikipedia is original research. However, English Wikipedia is more popular and there are much more people guarding the articles. So you should be very careful on English Wikipedia. When you're adding something to English Wikipedia from a source, try to minimize "modifications" to the equations, otherwise it can be labeled as original research and removed. You shouldn't "wait" with your contributions to English Wikipedia – it's not a place for original research; instead you should make an English mathematical blog (or write a book) where you can add as much original research as you want – I admire your work. A1E6 (talk) 15:03, 6 July 2022 (UTC)

Łukaszyk–Karmowski metric

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On the section 'Zeros, poles and symmetries' in the lemniscatic elliptic functions

I was wondering if there were more resources regarding the functions M(z) and N(z) -- particularly their infinite product form, defining differential equations and power series. I am still learning this subject and this seems very important.

I'm having some difficulty looking up Gauss's original work as well. And I will likely have to translate it.

I also did not see a source for the differential equation statement, so I thought to ask.

Thank you very much for your work. I've seen various edits to that page lately and I always excitedly look to see what's new. It's like a mathematical Christmas everyday. 15:55, 30 November 2022 (UTC)

It seems that the power series (and the differential equation) appear only in Gauss' original work. It's freely available here: (power series; there's an error on the page – the coefficient of

x^{5}

should be

-1/60

, not

-1/16

), (differential equation). A1E6 (talk) 17:15, 30 November 2022 (UTC)

Thank you very much! 23:18, 30 November 2022 (UTC)

Pi

Arbitrary-Angle Pendulum Fourier Series

Hi, I was wondering where you got the expressions for the amplitudes in the Fourier series for the pendulum. The closed-form expression given there in terms of Jacobi elliptic functions appears to have a slight mistake (it should be in terms of sn, not cd) and, after playing around in Matlab, I believe the coefficients of the Fourier series are also slightly off. I have not been able to find evaluations of the necessary integral. However, I'm a physicist doing nonlinear dynamics research and have a need to find accurate, closed-form expressions for these amplitudes. Thanks. 198.90.102.98 (talk) 23:10, 16 April 2023 (UTC)

No, it definitely should not be in terms of

\operatorname {sn}

. Because it can be easily seen that for small angles, the

\operatorname {sn}

version gives

\theta (t)\approx \theta _{0}\sin \left({\sqrt {\frac {g}{l}}}t\right)

, which doesn't agree with the small angle-approximation (i.e. with

\theta (t)\approx \theta _{0}\cos \left({\sqrt {\frac {g}{l}}}t\right)

). And since you're wondering where I got the expression from, I'll add a source to the article. By the way, I've also numerically checked everything with Mathematica and everything is OK. Are you sure that your Matlab code is correct? Please check again. A1E6 (talk) 11:14, 17 April 2023 (UTC)

The link you give shows the answer in terms of sn, but also explains the equivalence to cd -- apparently just a trig identity, they're related through the phase shift. So that works!

However, it doesn't give the Fourier coefficients, which is really what I'm wanting. Did you compute these yourself? I can see a way to obtain these as a Taylor series expansion (write the Fourier expansion for sn or cd, plug into the Taylor series for arcsin, expand, collect terms, do some trig polynomial reductions using double angle formulas, etc.) but this is a beast and I imagine this would just be to leading order?

I am actually working on some research in an area called Koopman theory and this has popped up as relevant. If you'd like to email me at agibson7@uccs.edu and discuss how you obtained these, I'd be happy to put you as a coauthor on a paper, should the project lead to one. In any case, I really need a reference specifically for the coefficients. If it's original research, that's fine, I just need to understand how they were found. 198.90.102.98 (talk) 01:47, 18 April 2023 (UTC)

I was confused about what you meant by "in terms of

\operatorname {sn}

". In case you meant

\theta =2\arcsin \left(k\operatorname {sn} \left({\sqrt {\frac {g}{l}}}t;k\right)\right)

, then that's wrong; but in case you meant

\theta =2\arcsin \left(k\operatorname {sn} \left({\sqrt {\frac {g}{l}}}t+\operatorname {K} (k);k\right)\right)

, then that's correct and it is indeed equivalent to the

\operatorname {cd}

formula.

Regarding your questions about the Fourier series coefficients: I didn't compute them myself and, unfortunately, I'm unable to find a reference supporting them.

However, you can try to contact the user who added the Fourier series (). Good luck! A1E6 (talk) 11:41, 18 April 2023 (UTC)

Thank you!

These coefficients turn out to have some rather significant implications for predicting the dynamics under forcing and for control, and methods for finding them for general integrable systems could be very useful. Hopefully I can either work it out myself or get in touch with the guy who did it. 198.90.102.98 (talk) 18:12, 18 April 2023 (UTC)

I've just found a proof of the Fourier series formula. I'll add the necessary references to the article. A1E6 (talk) 18:52, 22 April 2023 (UTC)

Jacobi theta function

Perhaps I should explain something. I really found these formulas out by researching these essays of Hermite, Glashan, Young, Runge, Prasolov, Solovyes and the others. I say the truth and I do not lie. The work Sulla risoluzione delle equazioni del quinto grado really contains the formula on exactly page 258 that gives the elliptic modulus for the nome q. You only have to solve this Bring-Jerrard-equation pattern after the modulus itself to get the value of the modulus. And you really have to only take this one formula to get the modulus and no formula else. I explain it to you exactly the way it is. And the formula of the hyperbolic functions of the fifth parts of the hyperbolic area functions is the direct result of the works of George Paxton Young and Carl Runge. The fifth root formulas do appear in their essays. I just displayed it by not using the fifth roots but by using the hyperbolic function formulas instead of that. And yes, I analyzed exactly their papers so that I could find out the fifth root formulas und it is not that original research to transform the fifth root formulas into hyperbolic formulas. And the identities of the Rogers Ramanujan continued fractions R and S lead to the Jacobi theta function formulas. Maybe I should say a special thing. Yes, some of the formulas do not appear directly in the now named essays. But the identities I used are well known identites that lead to these results in just a few steps. And therefore I really wonder myself that you call this already as a hundred percent original research, which is indeed not. We had this discussion once when we were talking about the Wikipedia article of the elliptic nome q function. It was exactly the same topic. I do not want to attack you. And I do not want to insult you either. I just want to explain you everything accurately. Hopefully I did not go too far with my sentences in this comment. I am not playing a crooked game with you at all. And I am not trying to outsmart you in any aspect. I just wonder myself all the time how you evaluate my work for such a long time in relation to the essay-technical aspect. Again and again I see, gradually more and more with concern and really serious astonishment, that you permanently title and evaluate my entries with the word original research. Do you really only recognize original research in my work? Can you really not see that it was only through the analysis of these works that I came up with the exact formulas I entered in the article Nome (mathematics) and in the article Theta function and in many more articles? I want to make sure you really do not get me wrong. I really do not want to mess with you. It just amazes me all the time how you react to my intensive entries in the Wikipedia articles. Maybe you should read the works and the results of the quintic equation researches of the mathematicians more carefully. Or maybe it simply helps that you can somehow better understand how I come up with these formulas that I have entered through comparatively easy thoughts. Maybe I am wrong myself and maybe it is not that easy to understand, if you did not dive into the material that deep and that long. Maybe I am such a fierce insider in this area that sometimes I do not see whether the other mathematical experts are following me or not. I do not want to show off. I just want to analyze myself in that point. Perhaps I have come to a point where it is a bit difficult for me to explain how I convert a given formula to a closely related formula. But it really is not the bare original research. The essays of the mathematicians were the fundament to work everything out and to write everything down. I really really hope now that I am not making you angry and that I am not driving you into rage. I simply wish that you can at least largely understand how I work and what encourages me to enter the elliptic formulas in this or that Wikipedia article. And I really hope that you still have a positive attitude towards me and that you do not reject me. And to be even more honest, I am extremely sorry that you are so concerned about my behavior and that my postings alarm you that much. I really do not want to play a game with you. I just wish that you understand me. I sincerely ask you to not delete anything. And hopefully we will always get along with each other. In fact, for the most part, I do like you indeed. And for the most part, I remember you positively. Only these warning signs really amaze me again and again in a questionable way. I honestly trust that we will get along well with each other also continuing and help us each other in different mathematical topics and that you will be successful in your studies and analyzes. Have a nice time and have good luck in all your studies! Yours faithfully and sincerely!! Lion Emil Jann Fiedler also known as Reformbenediktiner Reformbenediktiner (talk) 20:09, 2 June 2023 (UTC)

Yes, you are a fierce insider. According to Wikipedia rules, a non-expert should be able to see the equivalence between your work and the papers you cite (i.e. they should be able to verify your claims themselves). I doubt that this is the case. If you added the equations to a more popular article like the quintic equation or the Bring radical, it would be deleted straightaway. I do think that readers should be warned that what's in that section doesn't appear in the literature.

By the way, you surely know the

\varphi

and

\psi

functions from Bring radical#Other characterizations. They can be expressed by the theta function as follows:

\varphi (\tau )={\frac {\theta _{4}(-1/\tau )}{\theta _{4}(-2/\tau )}},\quad \psi (\tau )={\frac {\theta _{4}(\tau )}{\theta _{4}(2\tau )}}

where

\Im (\tau )>0

. You want to solve the quintic by theta functions, but we already have that on Wikipedia in the Bring radical article – it has proper citations and it gives all complex solutions of the quintic! I'm not going to delete your work, but I suggest that you delete it yourself. A1E6 (talk) 20:52, 2 June 2023 (UTC)

In any case, I am very happy and also very relieved that you treated me with mercy and did not punish me. I was reading the section Bring radical#Other characterizations in a careful and accurate way. And I saw one important thing. The sign in front of the linear term was negative to the sign of the quintic term in the Bring-Jerrard equation mentioned in that Bring radical article in exactly this section. But in the Bring-Jerrard equation I mentioned in the article Theta function and also in the article Nome (mathematics) the sign in front of the linear term was the same as the sign of the quintic term. And therefore we have another symmetry group of this Bring-Jerrard equation type and thus another way to solve the real solution. And so I sincerely ask you to allow me to keep my entries in the articles Theta function and Nome (mathematics) and not to erase it. Please accept it, I was really very meticulous, very thorough and very precise and did the most accurate custom work. I really plowed and brooded. I do not want to brag, but I treat the world of formulas with very great reverence and very great respect. I really see the mathematical formulas I put in as my gems and jewels. And I cut the gems and jewels until they reached a truly radiant brilliant cut. This brilliant cut has definitely been achieved. I know that for a fact. Unfortunately, all too often I have the weakness to find exactly those literature sources that prove everything even better than the sources that I had as a template to discover and produce all my formulas. But I have done what I could with this. And I want to make sure at all costs that the reader interested in elliptic functions knows exactly how to solve such quintic equations in general. And the reader should no longer wander around in a labyrinth that repeatedly shows him only sparsely and too abstractly how to solve the equations concerned. Instead of this, the reader should get such an article that shows him this solving of the quintic Bring-Jerrard equations in great accuracy and in every single detail, that the reader can use this as a template to immediately solve all these non-elementary solvable Bring-Jerrard equations exactly. The reader shouls know this in every single detail and I really want to make sure at all costs, that the reader knows the exact solution way of this equation accurate. This is really my heart's desire. With this I want to do a great favor for all people who really enjoy solving mathematical equations of higher degrees. Also the readers, who are strongly interested in elliptic functions, should be happy that they now finally know how exactly to use the Jacobi functions in great detail to solve the quintic equations. Because in these articles, which I have expanded, there are now steel molds that deliver the exact key bit. These formulas can be used like a safe stamp, which simply has to be printed and applied to the associated equation paper. That is exactly what I want to see achieved with it. If any mathematician or mathematically interested person would like to know how to solve qiuntic equations using elliptic functions, then they should not search for long and certainly no longer laboriously derive them from any overly abstract explanatory sources, but only the articles with the accurate detailed direct ones take the ready-made solution formulas, use the mentioned solution formulas as a mold and the solution is ready. This is the favor I would like to do for all of English-speaking humanity and for all people in general, so that all research on the elliptic solution methods of higher-degree equations is speeded up. And I remember myself as a teenager and young adult for so many months and years trying to figure out how to solve fifth degree equations. And I also remember searching through so many books and being thrown into one literary maze after another. After many years of waiting, I finally found the solution. Yes, I actually worked in exactly that way. Very often, like a nearly insane lover of mathematics, I get stuck on a few fringe problems and I will not rest nor rage nor give in until I really get to the solution, until I really find it out. This is surprisingly really my favorite way of exploring the mathematical world. But maybe I should confide in you one more specific thing that not all people know. There is one specific thing I am not even sure if exactly you know about that trait of me. Maybe I should mention it now. Perhaps I should mention this now so that you are no longer groping in the dark about me and my personality traits, but are also correctly informed about me and my mental nature and talent. I have Asperger's syndrome. This is a special kind of Autism. And I really have it. Very few people have Asperger's Syndrome and I have been diagnosed with it multiple times. Therefore, today there is no longer any doubt as to the fact that I really do carry this form of Autism in myself. In my eyes, Asperger's autism is one of the greatest gifts, even if you lack transversal competencies or organizational disciplines and information skills. As a carrier of Asperger's Syndrome, one often has a super-strong long-term memory, and also a strong declarative semantic and declarative episodic memory, as well as a great memory in relation to systems, patterns and structures. And that is exactly why I consider the Asperger's autism in me to be one of the greatest gifts of my entire life. I mean it extremely serious. By the way, this is also one of the reasons why I dream so much about mathematical formulas and also think about them so much, as if the world of mathematics is a safe island for me, like a protective zone in which I can be safe, secure and recovered, like in a magical holy land. Yes, that's me and that's my life. I am telling you the pure and clean truth. Now you really know me. Have a nice evening and a good night! Sleep very well! Have nice dreams! Yours faithfully and sincerely!! Lion Emil Jann Fiedler Reformbenediktiner (talk) 22:32, 2 June 2023 (UTC)

Thanks and have nice dreams as well! A1E6 (talk) 22:57, 2 June 2023 (UTC)

OK OK! I now clearly understood that I am not allowed to remove these template signs. I will be really careful from now on not to repeat this act. I will promise that very clearly and I will not break it. At first I thought that this sign was now obsolete. But apparently I still have not collected and included enough supporting sources. Do not worry! I will continue to look for supporting literature sources and singular references. But there is one question I will ask in a courageous way. From when or under what circumstances may the template sign be erased or disappear? I really have to seriously ask how far I can go and when I will cross red lines. I still say the truth. I do not want to mess with you. But sometimes I am not able to see what is allowed and what is not allowed. I am now leaving all template signs in place, as mounted by other Wikipedia users. In fact, I still was a bit scared that other users will come and remove everything I wrote down. Maybe I should now leave all articles in the way they are or leave these articles unchanged for a longer period of time. Perhaps this is really the time when some other Wikipedia users should first carefully analyze and review the articles I have enhanced. Maybe I should really let the other Wikipedia users examine and rate everything first and entrust them with the decision as to what to do with my entries. But I still very much hope that no user will make the decision to remove all the many formulas from me. That is still my biggest fear. Hopefully at least most of my formulas will survive. But I promise I won't touch anything more in these articles about theta function and the elliptic nome. From now on I keep my hands off in these articles. But I still have hope that nobody really deletes all my formulas. Yes, my fear still hovers over me like some kind of sword of Damokles. It would be a nightmare for me if some Wikipedia user actually came along and then made short work of all my formulas in this described destructive way. I will probably have to get used to these anxious thoughts a little bit. I really feel sorry for erasing the signs. From now on I will keep away from the two mentioned articles. I swear!! Lion Emil Jann Fiedler also known as Reformbenediktiner Reformbenediktiner (talk) 10:36, 5 June 2023 (UTC)

Note that your equations in that quintic section are not supposed to be there at all; a strict Wikipedian would delete them straightaway. I think that readers should know that the equations are your work. The template can be removed as soon as a non-expert reader can see equivalence between your equations and the equations in the cited papers. A1E6 (talk) 15:30, 5 June 2023 (UTC)

Allright! I understood everything. I won't touch anything anymore until I really have found corresponding literature sources and also corresponding singular references. I continue searching for the right information sources. And I keep my hands away from the articles Theta function and Nome (mathematics) completely. Maybe I should do one thing. Perhaps I should show you the found references at first. And If you give me green light, then I enter these references into the articles. If I stick to this concept, then there should not be any problems at all. Maybe I should really do it exactly that way. Yes, I align myself completely with this well designed concept. As soon as I find suitable sources, I will inform you about these sources on your discussion page. That should work in an optimal way exactly by these means. Now I know exactly what I have to do. Have a nice time! Yours faithfully and sincerely! Lion Emil Jann Fiedler Reformbenediktiner (talk) 17:25, 5 June 2023 (UTC)

Anyway, regarding the theta functions as functions of

q

instead of

\tau

(the period ratio) would be a sin because all the modular transformations take place in the

\tau

-space. In that sense, the nome is a redundant function if we define the theta functions in terms of

\tau

. As demonstrated in the Bring radical article, we can solve the quintic by theta functions without referring to the nome. A1E6 (talk) 21:49, 6 June 2023 (UTC)

Ok! I got this information. Now I have entered just a sentence into the article "Theta function". I mentioned the mathematician Karl Heinrich Schellbach and his work about the integer sequences with elliptic generating functions. But now I really keep away from this article and from the nome article too. I try to keep that promise. Reformbenediktiner (talk) 22:29, 6 June 2023 (UTC)

Elliptic nome

Greetings! I promised not to touch anything in the articles Theta function and Nome (mathematics) as I can remember clearly. But now I have a question. If I do not touch the section about the Quintic equations but do touch the other sections of these articles, am I allowed to change something? Do you allow me to add a derivation section for the elliptic nome values? And can I do it with the derivation of the theta function values in the Jacobi theta function article too? Or am I going too far again? Please answer me these questions honestly! Yours faithfully and sincerely! Lion Emil Jann Fiedler Reformbenediktiner (talk) 07:36, 10 June 2023 (UTC)

Of course, you're allowed to do that. A1E6 (talk) 11:45, 10 June 2023 (UTC)

I made it. Now I entered a complete derivation part into the article nome (mathematics) and I also described everything carefully. I really was extremely accurate and I even searched for documenting reference sources. I found some of them. But I proceed researching. I even found the references one. But I have to find them again. I found them already once, I say the truth. Therefore this is definitely not original research. I really say the truth, I do not lie, I had it once. But I have to find the reference sources again. And this will be an intensive search. But a few of the reference sources I even inserted in the moment, I wrote all these formulas down. Now I ask you in a faithful and sincere way to read the derivation and to analyze it. Hopefully you can understand the derivation of the nome values in a very good way. I ask you to do this. And I ask you a question. Is the combination of the theorems understandable in the described way? Please answer me this question honestly! My aim is to politely invite the regular reader on a journey of discovery of the elliptic nome function values. And I really hope that I am successful with this goal. Have a nice time and a lot of success in understanding the derivation of the nome values. Good day! Lion Emil Jann Fiedler from Bamberg Reformbenediktiner (talk) 04:00, 11 June 2023 (UTC)

I did it completely. Now I also entered the derivation of the theta function values in the article Theta function in a good readable way. And I described the Schwarz numbers and the Kneser numbers even more accurate. I also entered very good references that explain how I worked all these integer sequence explanations out. Perhaps you take a look at the theta function article. I ask you to do this and to say in an honest way if this is all allowed to stand in this article. I want to create a very good theta function article and a good nome article. And therefore I often use the German article as stencil that I created once in the German language and that I transfer in the English language now but I also improved all the formulas and the text in relation to the content so that there are brilliant explanations in the articles Theta function and Nome (mathematics) too. Now everything should look fabulous and gorgeous. Have a nice time! Lion Emil Jann Fiedler from Bamberg Reformbenediktiner (talk) 14:10, 13 June 2023 (UTC)

Theta function

Alright! Now I created and enlarged even more sections in the article Theta function and I am glad to be successful. Gradually this article is taking very clearly the form which it is intended to have. Already at this moment in my eyes this article looks excellent. I should say one more very important thing. In the last few days I have also added more references to the article so that the reader knows more about my sources of information. In the meantime, it has become an intensive routine for me that I consistently look out for suitable supporting literature sources and individual reference sources and search massively. But now I have a question to you. Do you think this article is still well structured and clear in the composition? And if yes, Do you think it is appropriate that I also describe the Pochhammer products and the partition number sequences in this article? Please answer me these questions in an honest way as always and tell me how I should possibly optimize the outline structure! I want to get secure that this article acquires excellent status or anyhow very welcome status. Please help me by giving me an accurate answer and by saying me in a righteous way what I have to do exactly! Yours faithfully and sincerely!! Lion Emil Jann Fiedler from Bamberg also known as Reformbenediktiner Reformbenediktiner (talk) 08:24, 25 June 2023 (UTC)

Yeah, you can add it. A1E6 (talk) 10:36, 25 June 2023 (UTC)

Even though it took a little longer time I finished my task at this moment. And I was very thorough again. I gave a lesson to more different partition number sequences. Now everything important about the partition numbers is entered in this article. Hopefully I did not produce any mistakes. At least I could not find any mistakes at all. My entries seem to be perfect. But if I see something that must be changed, then I will do this of course. I wish you a lot of pleasure with the reading of this article and have a nice time! Yours faithfully and sincerely!! Lion Emil Jann Fiedler from Bamberg Reformbenediktiner (talk) 11:39, 27 June 2023 (UTC)

And now I also have entered the integral formulas for the integrals from zero to one. It has to do with the Cauchy sums. In my eyes these integrals should be mentioned in the Theta function article. Therefore I inserted them too. This article gets even more brilliant and more brilliant. But if there is something missing or must be corrected, then please tell me about these aspects! Have a nice time!! Lion Emil Jann Fiedler from Bamberg also known as Reformbenediktiner Reformbenediktiner (talk) 04:35, 28 June 2023 (UTC)

Jacobi elliptic functions

ArbCom 2023 Elections voter message

Eckart conditions

Hi there. I guess I purposely do not hide my identity when I make Wiki edits since it hopefully gives credibility to what I write. The numerical example of the Eckart conditions given in the book by Jensen and myself (the reference to which you removed from this Wiki) has been found to be very helpful by many people. I suggest you read what we wrote in the book and see if you agree. Maybe after that you will reconsider the need to remove the reference. Have a nice day! Phil Bunker Bunkerpr (talk) 22:29, 21 September 2024 (UTC)

It will certainly look better if someone else adds it. Some people think that they are improving Wikipedia but they are wrong – in fact they violate Wikipedia policies by certain additions that are supposed to help people. It makes sense to help people but the rules are superior. So please be very careful if you are trying to re-add something. But one Bunker citation won't hurt anyone I guess. A1E6 (talk) 22:48, 21 September 2024 (UTC)

I will open a Talk page thread for you. A1E6 (talk) 23:01, 21 September 2024 (UTC)

Hi there Mr A1E6, What does it mean when you open a talk thread to me? I would be interested to have a discussion with you about the way many of my attempts at helping Wiki readers gets edited out. If the only reference to something helpful is to something written by me (such as is often the case with respect to permutation-inversion symmetry) what can I do?

Cheers Phil. Bunkerpr (talk) 13:41, 22 September 2024 (UTC)

Well, you should not add self-promo material. You should wait for some random, independent guy who happens to appreciate the material from your book and adds the content to Wikipedia. The fact that the material can be found only in your books can lead to your additions being challenged and removed – so, that's rather a bad thing; but if the information can be verified via multiple sources, that's better.

Here, by opening a thread I meant that the Eckart conditions article has now a Talk page and I drew attention to your references, so that people can independently decide whether your content is necessary/helpful etc. A1E6 (talk) 15:23, 22 September 2024 (UTC)

I hope you will not remove the reference to the article by M Schnell with whom I have no COI. Bunkerpr (talk) 16:30, 2 October 2024 (UTC)

It's OK. But please note that you should not be writing this in the Eckart conditions sections of my Talk page; you should have created a new section here called Molecular symmetry. A1E6 (talk) 00:28, 5 October 2024 (UTC)