Talk:Euler's constant

message: Is there a name for the conjecture that γ is transcendental?  --noösfractal 01:26, 7 August 2005 (UTC)
replies: text: No, it has no name.  However, if you prove it is transcendental it will probably be named AFTER you, like Apery's constant.  Whether its irrational is probably a more "answerable" question and is what most people are gunning for.  Hope you enjoyed my edits on this awesome number!  More is coming once I get my EDM.--Hypergeometric2F1[a,b,c,x] 14:22, 22 December 2005 (UTC)
thread_title:  Transcendental 

message: There's no reason to call this the Euler-Mascheroni constant instead of just Euler's constant. Euler defined it, proved that the limit in its definition exists, and then calculated it to 16 decimal places. Mascheroni eked out 3 more decimal places and gave it a new name; not exactly enough to have it named after him. Mathworld calls it the Euler-Mascheroni constant, but they are in the minority on this. Plenty of books and other sites call it simply Euler's constant, so there won't be any extra confusion by Wikipedia changing the name and then mentioning that some misguiding people mistakenly attribute the constant to Mascheroni. I don't know how to make changes to the title of an entry; maybe it's not possible without admin intervention. One option is to move the text over to Euler's constant and then redirect Euler-Mascheroni constant to there.
:But isn't Euler's constant more often used to refer to e rather than gamma ? Gandalf61 09:44, 2 March 2006 (UTC)
replies: text:  Some people do this, however, it is incorrect.  Having a clear cut note to that effect and a link to e would probably make sense. JoshuaZ 14:02, 2 March 2006 (UTC)
replies: text: Agree with Gandalf61, disagree with JoshuaZ. See List of topics named after Leonhard Euler; these are not the only two constants named after Euler. linas 00:47, 3 March 2006 (UTC)
replies: text:  Hmm, if the use denotation of e as Euler's constant is that common, then I withdraw my objection. Possibly a disambig page would still make sense? JoshuaZ 01:14, 3 March 2006 (UTC)
replies: text:  It looks like there are three constants named for Euler on that page: e, γ, and Ca. But even if there are more, it seems to make more sense to call them all "Euler's number" and refer to them with different symbols, rather than misattribute one of them to someone who didn't do anything significant with it. The only reason I could see to keep it this way is overwhelming convention (like with Venn diagrams), but as I said, it appears to be mostly just Mathworld and Wikipedia doing this at the moment, and authors who got their information from Mathworld or Wikipedia. --Pexatus 06:30, 3 March 2006 (UTC)
replies: text: It's not just Mathworld and Wikipedia. Havil writes that "Its full accepted name is the Euler-Mascheroni constant" (p. 90), despite acknowledging that Mascheroni's primary contribution was to cause other mathematicians trouble with his erroneous calculation. I prefer "Euler's constant" myself, but I think the current title is more appropriate for Wikipedia, not least for disambiguation purposes. Fredrik Johansson 08:47, 5 April 2006 (UTC)
replies: text: Practically speaking though, I think most people call this one Euler's Constant and e Euler's Number. Holomorph 12:50, 18 May 2006 (UTC)

text: Whatever the "official" terms are, some users looking for this Euler-Mascheroni constant would have trouble finding it in Wikipedia. For this reason I have just put a link to this article at the e article, and I hope it stays there. Noetica 23:27, 17 June 2006 (UTC)

text: More than a decade later, and the evidence presented here is no longer applicable, I think. Searching for "Euler's constant" in both Google and DuckDuckGo gives a mix of results, mostly referring to e, not γ. In what now passes for convention these days, asking ChatGPT a bunch of times about what Euler's constant is, it refers to e more times than γ.  cjquines  (talk) 23:20, 10 April 2024 (UTC)
thread_title:  Could the name be changed? 

message: I'm doing some work on Unicode related articles and I want to include a linkk from the Unicode character Eulers constant  (ℇ U+2107) to the appropriate artilce. However, upon seeing no mention of this notation in the article, I thought maybe I have the wrong constant. Any thoughts on this? Perhaps the article should mention this other notation (which in my fonts has no resemblence to gamma). Unicode includes Eulers constant as one of only three explicitly named constants with sa Unicode character devoted to it. Please let me know if there's another article that I should be looking for. Indexheavy 07:29, 1 May 2007 (UTC)
replies: text: Unicode 2107 looks like a curly capital E in my browser, so I suspect it is actually intended to denote Euler's number, not the Euler-Mascheroni constant. Not sure though why Unicode feel they need to introduce a special symbol for this - the standard notation is a lower case e. Gandalf61 10:10, 1 May 2007 (UTC)
replies: text: Unicode, especially earlier versions (character in question from v1.1, dating to 1993), does not seek to introduce anything. Instead it tries to encode things already in use, so there is a single standard. Evidently this stems from a Xerox standard, XCCS 353/046. I'm a bit perplexed by this symbol, myself. All I can infer is that the Xerox standard had a specialty symbol, a bit unlike anything Unicode already had encoded, and the Unicode guys thought "That difference may, in fact, be significant - better add it." As a font designer, I'd like to know what it originally referred to. I may choose to make it more "e"-like or "γ"-like in appearance. The glyph form typically used is very close to an upper or lower case open e (Ɛ, ɛ), which could have been used as a variant for the more usual closed e—though why Unicode wouldn't have just unified with one of those characters, I'm not sure. ⇔ ChristTrekker 17:00, 4 November 2014 (UTC)
replies: text: This is truly bizarre. Nevertheless, if I’m reading correctly the info in e.g. , this is a compatibility character with canonical decomposition to Ɛ (U+0190 LATIN CAPITAL LETTER OPEN E), hence you can’t go wrong by designing the glyph the same way.—Emil J. 14:23, 4 October 2022 (UTC)
thread_title:  Symbol for Eulers constant 

message: however the most mathematicians in world as : sorin radulescu ,marius radulescu, ene horia , dorel homentcovschi,lazar dragos ,univ,bucharest with mathematics faculty , albu thoma , t.zevedei , irina olteanu , solved the main problems as euler and radon- nikodym ,together optimal maitenance policy , in others trep ,problems ;this can be verified —Preceding unsigned comment added by 89.136.183.232 (talk • contribs) 
:Then please provide a reliable source for your claim, and also please take the time to write a clear and gramatical explanation, in English, of what you claim has been solved, how and by whom. Gandalf61 10:48, 2 June 2007 (UTC)
thread_title: Claim by anon contributor

message: I think the continued fraction representation in the infobox is more confusing then helpful. Only four places can fit in, and the way it's written makes it seems like there should be an obvious rule continuing this expansion, which of course there isn't. In the decimal/binary expansions, there are enough digits to make it obvious that the reader is not expected to be able to continue the sequence on his own. --Zvika 08:01, 5 September 2007 (UTC)
replies: text: I have gone ahead and added a disclaimer, as in Pi. I still think the continued fraction does not contribute much, but at least now it's not as misleading. --Zvika 05:06, 6 September 2007 (UTC)
thread_title:  Continued fraction representation in infobox 

message: Any post-2004 mathematician who thinks this number is likely rational?? Any numbers once conjectured to be irrational but now known to be rational?? Georgia guy 22:17, 6 October 2007 (UTC)
replies: text: see #Why gamma may be rational --84.130.141.54 (talk) 09:45, 6 June 2013 (UTC)

text: 2nd question: maybe Legendre's constant? --84.130.141.54 (talk) 09:48, 6 June 2013 (UTC)
thread_title:  Rational?? 

message: It says in the definition it is the difference between the harmonic series and the natural log, ln. Yet in the equation, it is represented as log(n). What's up with that? Nonagonal Spider (talk) 08:04, 24 November 2007 (UTC)
replies: text: The article follows the convention used by mathematicians, which is that log(x) means the natural logarithm unless another base is specifically mentioned. Gandalf61 (talk) 21:55, 24 November 2007 (UTC)
replies: text: It also uses ln in several references. Either way it should be consistent. Are any of the logs base 10? If not they should probably be changed to ln to increase readability. GromXXVII (talk) 00:10, 9 January 2008 (UTC)
replies: text: I've changed ln to log in the Asymptotic expansions section, so that at least this article is now internally consistent (I don't think we should change the occurences in the references section, as these are in the actual titles of published articles). There doesn't seem to be a consistent convention across Wikipedia mathematics articles for representing the natural logarithm function - Euler's totient function uses log; harmonic number uses ln; and Riemann zeta function uses both ! Wikipedia:WikiProject Mathematics/Conventions does not set a standard. Maybe this wider issue should be raised at Wikipedia talk:WikiProject Mathematics. Gandalf61 (talk) 11:11, 9 January 2008 (UTC)
replies: text: "Mathematicians" do not have a convention on the issue. The meaning of log varies with the local custom (across universities, departments, research environments and so on). As a matter of clarity, one should use either ln or loge for the natural logarithm, and log10 for the base-ten logarithm. Clarity is the name of the game. 80.202.223.150 (talk) 20:11, 16 January 2008 (UTC)
replies: text: Our logarithm article says "Mathematicians generally understand both "ln(x)" and "log(x)" to mean loge(x) and write "log10(x)" when the base-10 logarithm of x is intended". For another reference, see this Math Forum answer. This also coincides with my own experience - a typical mathematician will assume that log(x) means loge(x), whereas a typical engineer will assume that it means log10(x). I agree with you that it would be clearer if the base were always stated explicitly, but the correct place to suggest this in Wikipedia is at Wikipedia talk:WikiProject Mathematics. Gandalf61 (talk) 12:00, 17 January 2008 (UTC)
thread_title:  Natural Logarithm? 

message: In the section on properties, in the subsection on integrals, the article says "Indefinite integrals in which". The integrals are not indefinite. Perhaps the author means improper?  —Preceding unsigned comment added by 99.236.11.210 (talk) 05:36, 17 December 2007 (UTC)
thread_title:  Label for Integrals 

message: The infobox suggests that gamma is irrational, while this is unknown afaik.  —Preceding unsigned comment added by 86.93.56.14 (talk) 11:12, 18 February 2009 (UTC)
replies: text: You're right. — Emil J. 11:45, 18 February 2009 (UTC)
thread_title:  Irrational? 

message: In 1926, Vacca found:
:{
 \gamma + \zeta(2) = \sum_{k=1}^{\infty} \frac1{k\lfloor\sqrt{k}\rfloor^2}
  = 1 + \frac12 + \frac13 + \frac14\left(\frac14 + \dots + \frac18\right)
    + \frac19\left(\frac19 + \dots + \frac1{15}\right) + \dots 
}
or
:{
 \gamma = \sum_{k=2}^{\infty} \frac{k - \lfloor\sqrt{k}\rfloor^2}{k^2\lfloor\sqrt{k}\rfloor^2}
 =  \frac1{2^2} + \frac2{3^2}
  + \frac1{2^2}\left(\frac1{5^2} + \frac2{6^2} + \frac3{7^2} + \frac4{8^2}\right)
  + \frac1{3^2}\left(\frac1{10^2} + \dots + \frac6{15^2}\right) + \dots
}
(see Krämer, 2005)
[The first] Vacca's series may be obtained by manipulation of Catalan's 1875 integral.
------------
The correct series of Vacca is:
:\sum_{k=1}^\infty\left(\frac1{\lfloor \sqrt{k} \rfloor^2} - \frac1{k}\right) = \gamma + \zeta(2)
The error roots in the wrong typo of the online JFM. --Lagerfeuer (talk) 20:48, 28 July 2009 (UTC)
replies: text: Do you have a source? And what's "JFM"? — Emil J. 09:56, 29 July 2009 (UTC)

text: Well, the verification of that series (but not its source) is available at http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1578117#1578117 .  I think that the person who added that is likely Stefan Kraemer, and the source is again his 2005 thesis (or its extensions).  Incidentally, the link to that work is no longer dead. --24.34.22.136 (talk) 12:51, 29 July 2009 (UTC)
replies: text: When I wrote "source", I meant a reliable source according to WP standards which could be put in the article. I'm afraid the Art of Problem Solving forum does not meet the criteria. I have convinced myself that the derivation is correct, but a formal source is still needed. Krämer's thesis would be good enough, but we need to check that it really states it. You seem to suggest that it is available online; could you post the exact link? I gather that his website is back online, but I couldn't find a copy of his thesis there. — Emil J. 13:16, 29 July 2009 (UTC)

text: Thanks for the clarification. — Emil J. 10:08, 6 August 2009 (UTC)
thread_title:  Deleted stuff from the article 

message: Based upon a discussion at Wikipedia talk:WikiProject Mathematics#"Infoboxes" on number articles, I've removed the infobox from the article. If anyone disagrees, could you please join the discussion there. Thanks, Paul August ☎ 14:50, 18 October 2009 (UTC)
replies: text: I have suggested centralizing this discussion to Wikipedia_talk:WikiProject_Mathematics#Irrational_numbers_infobox and Wikipedia_talk:WikiProject_Mathematics#Infobox_with_various_expansions as it refers to an infobox occurring in several articles. Please go there to build consensus on this edit. RobHar (talk) 19:35, 18 October 2009 (UTC)
thread_title: Removal of infobox

message: I found out in 1993, that there is a typo in the well known article of James Whitbread Lee Glaisher (1872). He wrote:
Mascheroni has written only one paper about Euler's Constant (1790). He use only A. Comparing :de:David Bierens de Haan using A, Glaisher should be corrected with "De Haan and Mascheroni A; De Morgan, Boole, &c., have written it γ". There are a lot of early papers about the Integrallogarithm. Around 1800 there was a famous discussion about the constant of the Logarithmic integral function (which is equal with γ). For example, the german mathematician Carl Anton Bretschneider (1808-1878) use in his 1837-paper (1835) the symbol γ.
It is indefensible that Havil unaudited the claim of Glaisher has taken over with
An even more indefensible is that repeat these mistakes in the German translation (2007).
After long years I could't solve the main problem: What papers of De Morgan and Boole mentioned Glaisher? --Lagerfeuer (talk) 19:22, 23 October 2009 (UTC)
thread_title:  Symbol γ, Mascheroni (1790), Bretschneider (1835) and the article of Glaisher (1872)

message: Just to show how to solve for gamma in a cited article:
e^zeta[1]=2.5188167*(1+2+3+4+...n) as n goes to infinity 
where 2.51881667... = sqrt(2)*e^gamma
Doing an ln to both sides:
zeta[1] = ln(2.5188167) + ln(1+2+3+4+...n)
zeta[1] - ln(1+2+3+4+...n) = ln(2.51881667..)
Substitution sqrt(2)*e^gamma for 2.51881667
zeta[1] - ln(1+2+3+4+...n) = ln(sqrt(2)*e^gamma))
zeta[1] - ln(1+2+3+4+...n) = ln(sqrt(2)) + gamma
Formally,
:\gamma = \lim_{n \rightarrow \infty}\left [ \sum_{k=1}^n \frac{1}{k} - \ln \sqrt { \sum_{k=1}^n k } \right ] - \ln \sqrt 2
--Ryansinclair (talk) 13:58, 6 April 2010 (UTC)
replies: text: There is no reference to a published reliable source in the OEIS link, and neither it nor your derivation seem to make much sense. There is no such thing as zeta(1), to begin with. The final result is wrong, it is easy to see that the limit is divergent: \ln \sum_{k=1}^n k=\ln\left(\frac{n(n+1)}2\right)=2\ln n+O(1) and \sum_{k=1}^n \frac1k=\ln n+O(1), hence \lim_{n\to\infty}\left( \sum_{k=1}^n\frac1k - \ln\sum_{k=1}^n k \right)=\lim_{n\to\infty}(-\ln n+O(1))=-\infty.—Emil J. 14:31, 6 April 2010 (UTC)

text: \gamma = \lim_{n \rightarrow \infty}\left [ \sum_{k=1}^n \frac{1}{k} - \ln \sqrt { \sum_{k=1}^n k } \right ] - \ln \sqrt 2
I believe this formula does converge. It should be posted.
--Rsg4191984 (talk) 06:03, 12 January 2011 (UTC)
thread_title:  Solving for Gamma 

message: I came across this paper, which claims to prove that \gamma is irrational:
http://arxiv.org/abs/math/0310404
It doesn't seem to be referenced anywhere, is it bogus?
Pscholl (talk) 19:09, 21 April 2010 (UTC)
replies: text: It appears to have never been published in a peer-reviewed journal. ArXiv does not review correctness. I say, "bogus". Justin W Smith talk/stalk 22:20, 21 April 2010 (UTC)
replies: text: I agree. IMHO his handwaving at the end of 3.1 where he says \alpha \! and \beta \! have the same "attributes" is the problem. Mark Hurd (talk) 05:59, 24 November 2011 (UTC)
thread_title:  Proof of irrationality? 

message: See here. Count Iblis (talk) 01:07, 4 November 2010 (UTC)
replies: text: Not really, since from the appearance and ubiquity of this constant in very large number of mathematical formulas and theorems, it is likely to be an irrational number instead. The article itself does mention several progresses towarding the proof of its irrationality, in which an author show that if γ = a/b (where a,b are positive integers) then the denominator would be unusually immense (larger than 10^244663). However, the case that γ is rational cannot be currently ruled out with confidence =)). 2402:800:63AC:BE7D:D056:F908:8ED1:3853 (talk) 10:30, 7 August 2023 (UTC)
thread_title:  Why gamma may be rational 

message: I was wondering if there was any particular reason why the hurwitz zeta function is used here instead of either bernouilli numbers or the values of the zeta function at the negative integers? From what I can tell, Euler would have derived this from the Euler-maclaurin formula to begin with, which would have involved bernouilli numbers rather than the hurwitz zeta. I have no particular problems with the hurwitz zeta, I'm just wondering why it seems to have been given preference over what would be a more recognisable expansion.  — Preceding unsigned comment added by 92.10.241.81 (talk) 21:13, 9 June 2011 (UTC)
thread_title:  On the inclusion of the hurwitz zeta function in the rational zeta expansion 

message: After "fixing a double redirect" this mysterious character redirects here. But its appearance is not like γ. Any thoughts, which of Euler's constants it should signify? Incnis Mrsi (talk) 15:43, 9 January 2012 (UTC)
replies: text: Perhaps they were thinking of Euler's number? —Mark Dominus (talk) 17:02, 9 January 2012 (UTC)
replies: text:  I newer saw such a symbol for e, which is always written with a loop, i.e. as lowercase Latin E. Should we consult WikiProject Mathematics or so? Incnis Mrsi (talk) 17:44, 9 January 2012 (UTC)
replies: text: This discussion has been around for quite awhile. ⇔ ChristTrekker 17:03, 4 November 2014 (UTC)
thread_title:  [[ℇ]] (U+2107 EULER CONSTANT) 

message: Cramér's_conjecture#Heuristic_justification
Prime_gap#Lower_bounds  — Preceding unsigned comment added by Reddwarf2956 (talk • contribs) 19:28, 20 September 2013 (UTC)
thread_title:  Two more Appearances 

message: I think it would be nice to include at least single proof of the existence and finiteness of the limit in the definition.  — Preceding unsigned comment added by 88.103.38.103 (talk) 10:07, 20 December 2013 (UTC)
replies: text: I agree, this would be a good idea.  One way I like to explain it to students is using an image similar to the first image of the article, showing that the blue area is finite by using upper and lower sum approximations to the Riemann integral of 1/x as a cute application of those ideas as well.  I don't really have the time to write this up myself, but it would definitely make a worthy addition to the article.  Sławomir Biały (talk) 16:20, 20 December 2013 (UTC)
thread_title:  Existence 

message: The Euler-Mascheroni constant appears also in the probabilistic prime counting formula which can be represented as follows:
\pi(x=p_i)=\alpha.\int_2^x\prod_{i=2}^{x=p_i} (1-1/p_{i}).dx \ with \  \alpha\approx1.7810292
where \alpha can be very closely approximated as:
\alpha=e^\gamma \ where \  \gamma\approx0.57721 \ is \ the \ Euler-Mascheroni constant
The origin of this formula can be found here.
Chrisdecorte (talk) 18:48, 24 February 2014 (UTC)
thread_title:  Euler-Mascheroni constant in probabilistic prime counting formula 

message: Is this statement below correct?
Series of prime numbers:
:\begin{align} \gamma = \lim_{n \to \infty} \left( \ln n - \sum_{p \le n} \frac{ \ln p }{ p-1 } \right)\end{align}. 
I just removed the reference to Mathworld because there is nothing at the location that looks like the statement above. Also, is the math correct?
:It seems to be true numerically (although convergence is very slow).  There's probably a clever way to get it from Mertens' theorem.  Sławomir Biały (talk) 22:28, 12 April 2015 (UTC)
replies: text: I guess then the question really is: Correct reference with proof? John W. Nicholson (talk) 23:02, 12 April 2015 (UTC)
replies: text:  Well, knowing that it's true suggests that it should be reference-able.  Obviously, a reference would be ideal.  Sławomir Biały (talk) 01:16, 13 April 2015 (UTC)
replies: text:  I looked at the Mathworld reference, and it seems like the result is obtained by taking equations (15) and (17), and equating the right-hand sides, then using the geometric series expansion of p/(p-1).  Sławomir Biały (talk) 12:16, 13 April 2015 (UTC)
thread_title:  Is this statement correct? 

message: The nth factor is said to be the (n+1)st root of an expression, but this expression appears to be a number rather than a function, so it doesn't have "roots". So what is the correct formula for the nth factor in this expression? I tried looking up the papers of Ser and Sondow referred to below the formula, but I can't find Ser's paper, and I can't find where in Sondow's paper the relevant formula is supposed to be. David9550 (talk) 10:55, 20 September 2015 (UTC)
replies: text: See nth root. SławomirBiały 11:10, 20 September 2015 (UTC)
replies: text: Oops, I guess I forgot some words have multiple meanings! Thanks for the clarification. David9550 (talk) 14:36, 25 September 2015 (UTC)
thread_title:  Error in product formula for <math>e^\gamma</math> ? 

message: Substituted at 02:04, 5 May 2016 (UTC)
thread_title: Assessment comment

message: From the image it seems it should be ceiling function. Floor is always smaller than the original function, so this value would be negative: \int _{1}^{\infty }\left({\frac {1}{\lfloor x\rfloor }}-{\frac {1}{x}}\right)\,dx--Reciprocist (talk) 04:14, 20 October 2016 (UTC)
replies: text: Note the reciprocals.  When j < x, you get 1/j > 1/x.  Joule36e5 (talk) 09:36, 29 October 2016 (UTC)
thread_title:  Floor function? 

message: I am curious why this notation is used in the graphic at the head of the Generalizations section, while it is not mentioned at all in the text and seems to be redundant. A brief search on Wolfram Mathworld and the internet in general suggests that this notation is not used anywhere in the literature and may be, as far as I can tell, something that was invented by the person who created that image. Xolroc (talk) 14:51, 26 March 2017 (UTC)
replies: text: I think it's just notation.  A better image could certainly be added, without the notation in the graphic.  Sławomir Biały (talk) 15:26, 26 March 2017 (UTC)
replies: text: My main complaint about it is not that it is wrong per se, but that the abm notation doesn't seem to be used anywhere else. If it was accepted alternative notation I'd be fine with it, but the fact that it doesn't show up on Mathworld and a few google searches turn up nothing suggests that the notation is not in common use. If I could figure out how to get Mathematica to generate such an image I probably would replace it with a plot of γα, but for the moment I'm not able to. Xolroc (talk) 00:59, 27 March 2017 (UTC)
replies: text: Plot[HarmonicNumber[n, -x] + (n^x (n^(-x) - n))/(1 + x) /. n -> 1000000, {x, -4, 0}, PlotRange -> {0, 1}] This is at least sufficient for illustration purpose. Convergence is unfortunately slow around and above the minimum, but with a larger n the expression will become very slow to evaluate. Ylai (talk) 11:46, 8 October 2017 (UTC)
replies: text:  I executed the above code and found that the result figure is different from the current one on the wiki page. The function is much more straight in the range x<-0.5, but I am not sure if it is because of the slow convergence of the function. 140.112.54.158 (talk) 01:09, 6 March 2018 (UTC)
thread_title:  abm(x)? 

message: If you want to do some work on the references in this article, and you've done a great job so far, all parenthetical citations should be converted to footnotes. Parenthetical citations were deprecated sometime after I did my adjustments. – Finnusertop (talk ⋅ contribs) 15:00, 23 April 2021 (UTC)
thread_title:  Citation style 

message: I think "ln" is a better notation than "log" for the following reasons:
*Consistency: At present this article uses both log and ln.
*Clarity: ln is unambiguous contrary to log.
*Compliance with standards: ln is probably more widely used, and recommended by ISO.
The only argument in favor of "log" seems to be that "log" is more accepted in the field of number theory. I think this argument weighs less than the previous two, all the more so since this article is not really about number theory.2A01:CB00:A34:1000:ED0E:D7C1:D5BD:64BC (talk) 14:00, 13 June 2021 (UTC)
thread_title:  "Log" vs "Ln" 

message: Examination of the references cited in the article, and the entries in the "further reading" and "external links" sections indicates that the substantial majority of them call this number "Euler's constant", with "Euler–Mascheroni constant" being rare. This confirms my own impressions, and also what I have found by internet searches. γ is normally referred to in English as "Euler's constant", rarely as the "Euler–Mascheroni constant" Nobody seems to have advanced any compelling reason for making this article an exception to the normal practice of using the name most commonly used and understood in English. (To avoid any possible misunderstanding, e is normally called "Euler's number", not "Euler's constant".) I shall therefore move this article from the title "Euler–Mascheroni constant" to "Euler's constant". JBW (talk) 21:36, 22 September 2021 (UTC)
thread_title: Euler's constant

message: started an edit war by insisting to have "Mathematical constant" as a short description. This is simply a definition of the second word of the title, and so, does not fulfill any objective of a short description, and breaks WP:SDNOTDEF ("avoid duplicating information that is already in the title"). In particular, it does not disambiguates this article from Euler's number, which is another mathematical constant.
The short descriptions that  reverted was firstly "Mathematical constant relating logarithm and harmonic series", which is effectively too long (60 characters). The second reverted version is "Relates logarithm and harmonic series" (37 characters). It respects WP:SDSHORT. It fulfills completely the purpose of short descriptions:
* For readers not interested in mathematics, the terms  "logarithm" seems sufficient for saying that the article is not for them.
* For possibly interested readers, it clearly indicates the area of mathematics that is involved.
* It disambiguates from Euler's number, which is another mathematical constant with a similar name.
So, I'll restore this short description, since the balance between arguments is clearly in its favor. D.Lazard (talk) 13:46, 6 February 2022 (UTC)
replies: text: I maintain that « Relates logarithm and harmonic series » is an incorrect and cryptic hint to what the described object might be. It is incorrect because gamma is just one of the terms of a relation including the logarithm and a partial sum of the harmonic series: this doesn’t confer to it the exclusive property of « relating » the two notions. But what is much worse is that it is cryptic, because it doesn’t include an essential information: that it is a constant. It is like describing Cicero with the  statement «  Opposed the Catilinean conspiracy », without mentioning the essential fact that he was a Roman statesman.--Sapphorain (talk) 15:19, 6 February 2022 (UTC)
replies: text: "it doesn’t include an essential information: that it is a constant": This information is in the article title. No need to repeat it in the short description. For the other points, let wait the opinion of other editors, and if other editors do not give their opinion here, ask at WT:WPM where a long discussion occurred recently on short descriptions in mathematics. D.Lazard (talk) 17:42, 6 February 2022 (UTC)
thread_title:  Short description 

message: h t t p s://v i x r a .org/pdf/1208.0009v3.pdf#:~:text=%3A%20The%20Euler-,Mascheroni%20constant%20is%20irrational. (remove the spaces because of blacklist)
TRANSCENDENTAL I am a Green Bee (talk) 14:55, 29 July 2023 (UTC)
replies: text: This article is blatantly wrong. Apparently the author ignores that an infinite limit is neither rational neither irrational. D.Lazard (talk) 15:52, 29 July 2023 (UTC)
thread_title:  transcendental :(  I hate infinite decimals :( :( :( 

message: Is the beta function fomula given in "relation to the gamma function" here:
\begin{align} \gamma &= \lim_{n\to\infty}\left(\frac{ \Gamma\left(\frac1{n}\right) \Gamma(n+1)\, n^{1+\frac1{n}}}{\Gamma\left(2+n+\frac1{n}\right)} - \frac{n^2}{n+1}\right) \\
&= \lim\limits_{m\to\infty}\sum_{k=1}^m{m \choose k}\frac{(-1)^k}{k}\log\big(\Gamma(k+1)\big). \end{align}
missing a minus sign? When I inputted the equation into Desmos, it converged to negative \gamma instead of \gamma. 77551enpassant (talk) 16:57, 9 October 2023 (UTC)
thread_title:  Formula