Talk:MRB constant

Why is this remarkable?

I'd be interested in any sort of proof that this infinite sum was not something evaluable in closed form. But since that kind of result is what one would generally expect, I'm somewhat at a loss to understand what is remarkable about this constant. Am I missing the point? Charles Matthews (talk) 21:34, 8 May 2009 (UTC)

The series $\sum _{k=1}^{\infty }(-1)^{k}k^{1/k}$ diverges. Remarkable is that its partial sums are bounded. And the MBR constant is simply the upper limit for them. Maxal (talk) 00:39, 28 August 2009 (UTC)

The question is not answered, nor is the claim that anyone other than "MRB", himself, uses the name "MRB constant". — Arthur Rubin (talk) 17:35, 10 January 2015 (UTC)

Dear Arthur Rubin, before you delete the MRB constant article, you might want to find out that MathWorld uses the term MRB constant that Simon Plouffe coined. It uses it Here http://mathworld.wolfram.com/MRBConstant.html , here http://mathworld.wolfram.com/SteinersProblem.html , here http://mathworld.wolfram.com/PowerTower.html , and mentions work done on it here http://mathworld.wolfram.com/IrrationalNumber.html , and here http://mathworld.wolfram.com/NormalNumber.html . The The wikipeida aticle, MRB constant, was written by User Eustress, and has been edited by at least 5 people, see https://wiki.riteme.site/w/index.php?title=MRB_constant&action=history .

The MRB constant article had 9381 visits in December; see http://stats-classic.grok.se/en/201412/MRB%20constant , On Dec 4 it had more visits than pi did; compare http://stats-classic.grok.se/en/201412/Pi with http://stats-classic.grok.se/en/201412/MRB%20constant .

The MRB constant is on Googke Scholar here http://scholar.google.com/scholar?hl=en&q=%22MRB+constant%22 , where you can find out it is mentioned by name in the following scholarly article found here http://arxiv.org/pdf/0912.3844v3.pdf . The MRB constant is referred to In Steven Finch's book Mathematical Constants as , as found here http://books.google.com/books?id=Pl5I2ZSI6uAC&printsec=frontcover#v=onepage&q=a%20more%20difficult%20evaluation%20concerns%20the%20series&f=false . You can find that on page 450\, where the bookmark [17] mentions the name M. R. Burns!

The MRB constant is used by Wolfram alpha as you can find out here http://www.wolframalpha.com/input/?i=mrb+constant&a=*C.mrb+constant-_*NamedConstant- and here http://www.wolframalpha.com/input/?i=mrb+constant&a=*C.mrb+constant-_*MathWorld and here http://www.wolframalpha.com/input/?i=0.187859642 .

Before you delete it, you at least need to come up with a better excuse than, "The question is not answered, nor is the claim that anyone other than 'MRB', himself, uses the name 'MRB constant'. " Marvin Ray Burns (talk) 23:14, 10 January 2015 (UTC)

Neither Mathworld nor Wolfram Alpha is considered a "reliable source" for names or for significance. Possibly one of the books you mentioned might be satisfactory. — Arthur Rubin (talk) 03:02, 11 January 2015 (UTC)

I'll write more when I get home; typing on a smartphone can be a real pain. — Arthur Rubin (talk) 05:19, 11 January 2015 (UTC)

The MRB constant is referred to (not by name) on page 450 of Steven Finch's book Mathematical Constants. The endnote mentions your unpublished work, "M. R. Burns", but not the name of the constant. I'll recheck the references in the article, but I haven't seen a plausible claim of notability. You are permitted to remove the PROD tag, but not a "notability" tag. — Arthur Rubin (talk) 07:47, 11 January 2015 (UTC)

The MRB constant is also mentioned by name in Unified algorithms for polylogarithm, L-series, and zeta variants by Richard E. Crandall1 March 26, 2012 (published by PSI press, which is no longer in operation). However, I have made it available here http://www.marvinrayburns.com/UniversalTOC25.pdf . — Preceding unsigned comment added by Marburns (talk • contribs) 14:33, 11 January 2015 (UTC)

Here is where Simon Plouffe used the name http://www.plouffe.fr/simon/articles/Tableofconstants.pdf .Marvin Ray Burns (talk) 14:50, 11 January 2015 (UTC)

I've been relying on other people to name the constant since 1999. However, since I am the original investigator, hence discoverer, of the constant I have some prerogative to name it,Marvin Ray Burns (talk) 15:03, 11 January 2015 (UTC)

I quote from the general notability guideline, "It is a generally accepted standard that editors should attempt to follow, though it is best treated with common sense, and occasional exceptions may apply." You agree that the series, itself" is notable from Finch. Further I have shown that other places used the name. I quote from the guidelines, "Information on Wikipedia must be verifiable; if no reliable third-party sources can be found on a topic, then it should not have a separate article." Finch is a reliable third-party source on the topic, as Used by Mathworld as a reliable third-party source for the MRB constant.

Again I quote from the guidelines:

Notability guidelines do not apply to content within an article.

The criteria applied to article creation/retention are not the same as those applied to article content. The notability guidelines do not apply to article or list content (with the exception that some lists restrict inclusion to notable items or people). Content coverage within a given article or list (i.e., whether something is noteworthy enough to be mentioned in the article or list) is governed by the principle of due weight and other content policies."

What you are holding off in not accepting the article is the name of the constant. In the article, where it explains where the name comes from, there is a reference to Plouffe's list of constants where he named the MRB Constant. Also, I have definitely shown above there is due weight of evidence that the name is used by other people, in other places (where, "The notability guidelines do not apply to article or list content." )

This should be sufficient reason for common sense to be used to treat the guidelines in such a way that the article, with that name, should stand.

Again you agree that the subject itself is notable; If nothing else, we should use another name for the article. However, the only name used for it is the MRB constant.Marvin Ray Burns (talk) 18:37, 11 January 2015 (UTC)

Mathematically the series is "The Alternating Sum over (-1)^x*(x^(1/x)-1) between 1 and infinity," which is a little to wordy for a good title, Finch used the term "The series Limit...," again, this is to wordy to make a good title.Marvin Ray Burns (talk) 18:54, 11 January 2015 (UTC)

Well, no, I don't agree that the series, itself, is notable. I agree it exists, but WP:GNG almost certnaily will not work. If it doesn't meet WP:GNG (which is almost impossible for a mathematical constant), per WP:NUMBER#Irrational numbers, the "requirements" are:

1. Is there a book about this irrational number, or at least a great number of papers using this number?
2. Are both the decimal expansion and the continued fraction of this number listed in the OEIS?
3. Is this number listed in a book such as Finch's Mathematical Constants?
4. Is there at least one commonly accepted name for this irrational number?

Analysis:

1. Your Google scholar search above produces 2 preprints (the middle one, for me, is an archive of a Mathworld entry pointing to the Mathworld article on the number.) I realize "a great number of papers" is subjective, but I would accept 10 papers published in refereed journals, for the moment. (There is a pseudomathematician who I will not name here who created his own journals to publish his own work. That does not make the work notable, but the fact that he did it was a factor in determining that he was notable. I'm not suggesting you would do that, but, if others were to do that, it still wouldn't make the constant notable.)
2. Good.
3. Good.
4. Well, so far, we only have Mathworld, possibly Wolfram Alpha, and Simon Plouffe's web page. ...and OEIS entries, some of which are partially authored by MRB. (added after comments below).

For what it's worth, I worked on Erdös' sum-distinct set constant while I was at JPL, and I would not be in favor of that article being here, either. (I read a Russian-language paper which purported to show the constant (in fact, to use Finch's notation, $\lim _{n\to \infty }{\frac {v_{n}}{2^{n}}}$) was 0, but it improperly took the limit of a sum to be the sum of the limits.) — Arthur Rubin (talk) 22:20, 11 January 2015 (UTC)

The rationale for the "Notability (numbers)" page has to do with whether many people are likely to look up a certain number. And the MRB constant article has been viewed a great number of times! Using their examples, I would say, that the name MRB constant is closer to 42 than the "square root of 40887."

The OEIS does mention the MRB constant by name in (sequence A160755 in the OEIS) and (sequence A173273 in the OEIS) and an OEIS search for "MRB constant" also gives (sequence A052110 in the OEIS) and of course (sequence A037077 in the OEIS).Marvin Ray Burns (talk) 01:06, 13 January 2015 (UTC)

I'm willing to concede point 4, although it appears "MRB" is the author of some of the entries in OEIS, and I'm not sure how much COI-notability-checking they do. However, point 1 still needs more work. — Arthur Rubin (talk) 23:51, 13 January 2015 (UTC)

It's worthy to note that I can not publish just what I want: the OEIS entries go through a checking process by trained individuals.For s sample of the process see the draft at https://oeis.org/draft/A248660 (before it is approved, modified or denied).Marvin Ray Burns (talk) 16:41, 14 January 2015 (UTC)

Irrationality

• If irrationality is not proved, it has to be stated as such. It is at least misleading to call a number irrational if its irrationality is not proved. Maxal (talk) 11:30, 26 January 2011 (UTC)
  • Per WP:AB, in clear-cut case, I corrected the statement concerning irrationality.Marvin Ray Burns (talk) 20:10, 1 February 2011 (UTC)

Comments on rewrite

Although I still don't see notability as established, (nor do I see the symbol used in mathematical constants sourced), do you mind if I work on the rewrite?

At first glance, problems I see include the Mathworld entry being used more than once (should have the same reference), and MRB's "mathematical binge" seems not to be reliably sourced. I'm afraid we would need a source other than MRB, as it doesn't really seem to fit under WP:SELFPUB.

And it still only has limited evidence the constant is often used by other than MRB. — Arthur Rubin (talk) 00:04, 14 January 2015 (UTC)

Please do help work on it. I would like to keep some of the references that you might think aren't as notable as they should be; if there are better ones, I don't mind them being replaced. The math binge might be able to be replaced with something about my unpublished note to Finch. Thank You.Marvin Ray Burns (talk) 16:32, 14 January 2015 (UTC)

I found an URL to Crandall's paper that does not involve my website.

I noticed something new on RICHARD J. MATHAR's reference for his definition of the MRB constant. Here it is in full: "18. Neil J. A. Sloane, The On-Line Encyclopedia Of Integer Sequences, Notices Am. Math. Soc. 50 (2003), no. 8, 912–915, http://www.oeis.org/. MR 1992789 (2004f:11151)." Is that "Notices Am. Math. Soc. 50 (2003), no. 8, 912–915" and "MR 1992789 (2004f:11151)" a new reference giving more notoriety to OEIS entries?Marvin Ray Burns (talk) 01:31, 15 January 2015 (UTC)

Also concerning using Euler summation being successful in accelerating the convergence of the MRB constant, he gives the reference "G. H. Hardy, Divergent series, 2 ed., Chelsea Publishing Company, 1991. MR 1188874 (93g:01100)." It is online at https://ia700707.us.archive.org/23/items/DivergentSeries/Hardy-DivergentSeries_text.pdf .Marvin Ray Burns (talk) 02:25, 15 January 2015 (UTC) Some of the math Hardy uses to prove convergence and acceleration, perhaps, could be applied to "Method(s) of accelerating the convergence of the MRB constant." And we would have a nice source for it! Crandall gave two methods of accelerating its convergence also.(I don't know the proofs of Crandalls acceleration methods, but they are bound to come in part from reliable sources! Marvin Ray Burns (talk) 02:48, 15 January 2015 (UTC)

"http://mathworld.wolfram.com/topics/MiscellaneousConstants.html" is not a "table of mathematical constants ... in the United States". I can't speak for the other lists, especially the ones not published in English. And some of the suggestions you're making above relate to proposed publications about the constant, which would be inappropriate for Wikipedia until published. The particular acceleration methods to be applied to the series should actually be used in a publication, before mention is made here, even if you and I would agree that the acceleration methods would work better. — Arthur Rubin (talk) 03:06, 15 January 2015 (UTC)

The acceleration methods are used in Crandall and Mathar and mentioned by Finch; does that help?Marvin Ray Burns (talk) 12:56, 15 January 2015 (UTC)

"Notices Am. Math. Soc. 50 (2003), no. 8, 912–915" is probably a review of OEIS is an article by Sloane about the OEIS, available online at http://www.ams.org/notices/200308/comm-sloane.pdf ; "MR 1992789" is a Math Reviews index, and "2004f:11151" is some sort of a citation identifier, unlikely to be useful here. You can ask further questions about what that means on WT:MATH. I don't see any possibility of it being usable on Wikipedia except in the article on OEIS. — Arthur Rubin (talk) 03:11, 15 January 2015 (UTC)

Proposed rewrite with more use of references and less reliance on name

Marvin R. Burns, the constant's original investigator, in 1999

This mathematical constant is sometimes called the MRB constant or MRB.. MRB stands for Marvin Ray Burns. Being a sum of irrational numbers its irrationally remains an open problem.

The numerical value of the constant, truncated to 6 decimal places, is

0.187859… (sequence A037077 in the OEIS).

Definition

First 100 partial sums of (-1)^k (k^{1/k} - 1)

The constant is related to the following divergent series:

$\sum _{k=1}^{\infty }(-1)^{k}k^{1/k}.$

Its partial sums

$s_{n}=\sum _{k=1}^{n}(-1)^{k}k^{1/k}$

are bounded so that their limit points form an interval [−0.812140…,0.187859…] of length 1.. The upper limit point 0.187859… is what is sometimes called the MRB constant. The constant can be explicitly defined by the following infinite sums:

$0.187859\ldots =\sum _{k=1}^{\infty }(-1)^{k}(k^{1/k}-1)=\sum _{k=1}^{\infty }\left((2k)^{1/(2k)}-(2k-1)^{1/(2k-1)}\right).$

There is no known closed-form expression of this constant.

History

Marvin Ray Burns published his discovery of the constant in 1999. The discovery is a result of a "math binge" that started in the spring of 1994. Before verifying with colleague Simon Plouffe that such a constant had not already been discovered or at least not widely published, Burns called the constant "rc" for root constant. At Plouffe's suggestion, the constant was renamed Marvin Ray Burns's Constant, and then shortened to "MRB constant" in 1999. Since then it has been added to tables and lists of constants in a few countries, including Turkey, Iran, Germany. , the United States. and Italy

References

References

External links

• (sequence A037077 in the OEIS)

Category:Mathematical constants Category:Number theory

Link was dead and slightly off topic

In clear-cut case, Previous link was dead and slightly off topic: Well documented that the upper limit "is what is known as the MRB Constant." If anyone else wants to make a constuctive change, please do so. — Preceding unsigned comment added by Marburns (talk • contribs) 17:56, 28 January 2015 (UTC)

Countries

A web page being associated with a "country" is usually irrelevant. Wolfram's headquarters is located in the US, but it would be incorrect to state that something on their web page is associated with the US. Other examples include a French blogger (writing in English), and pages in languages I cannot read. It might be relevant to note that it's described in different languages, not apparently translations. I still question notability, and that sentence, in either form, does not support notability, nor does it seem interesting. — Arthur Rubin (talk) 23:07, 3 February 2015 (UTC)

Thanks for your explanation. I put it in there, manly, to fight the idea that I am the only one who uses the term MRB constant. I wanted to show that it was used in a lot of places, by a lot of other people! Marvin Ray Burns (talk) 02:49, 4 February 2015 (UTC)

WP:NUMBER#Irrational numbers

I don't think WP:NUMBER#Irrational numbers is the best standard to judge the MRB constant's worth of being able to have its own article, because the MRB constant is just not another irrational number like "Examples The square root of 2, (sin 1)2." They are elements of specific sets set forth by WP:NUMBER#Irrational numbers that are KNOWN irrationals (some roots, certain trig functions, and perhaps given logarithms), thus under the purview of WP:NUMBER#Irrational numbers. While the MRB constant (its series at least) is, according to Finch, an element of the set of iterated exponential constants; in this case, not known to be irrational. Marvin Ray Burns (talk) 03:12, 4 February 2015 (UTC)

I think the MRB constant should be judged by the "Notability of kinds of numbers' rationale" from Wikipedia:Notability (numbers):

Notability of kinds of numbers[edit] Examples Complex numbers. Transcendental numbers containing only 3s and 7s in their hexadecimal representations. The questions to ask are:

Have professional mathematicians published papers on this kind of number, or chapters in a book, or an entire book about this kind of number? Do MathWorld or PlanetMath have articles on this kind of number? Is there at least one commonly accepted name for this kind of number? An affirmative answer to these three questions indicates that this kind of number is notable enough for Wikipedia to have an article about it.

In some cases, notability guidelines for sequences of numbers might be more applicable, especially when it is straightforward to put the numbers in some kind order, such as ascending order.

Disposition of examples There exists at least one book titled Complex Numbers, one by Walter Ledermann, and several others with titles of the form Complex Numbers and somethingelse, such as Estermann's Complex Numbers and Functions. Both PlanetMath and MathWorld have articles on complex numbers. The name "complex number" has been almost universally accepted since mathematician Carl Friedrich Gauss coined it. Hence, complex numbers are notable enough for Wikipedia. On the other hand, transcendental numbers containing only 3s and 7s in their hexadecimal representations lack a commonly accepted name, in part because the description is so long, but mainly because hardly anyone, professional or amateur, has cared to study these numbers, much less publish anything about them.

I say that because of the "Rationale" section: Rationale[edit] The subset of numbers anyone could look up in Wikipedia is very small. And if we strike out those numbers that will only be looked up only out of curiosity on whether or not Wikipedia has an article about that number, we're left with an even smaller subset. That subset, give or take a few members, is exactly the same subset WP:NUM calls for. For example, many people will look up forty-two to genuinely learn more about it, while someone would look up the "square root of 40887" only to see if Wikipedia has an article about it and nothing else. No one would be able to specifically look up an integer at some inconvenient distance between 15 googolplexes and 16 googolplexes. I just felt it was an injustice from the beginning and am, just now, able to describe why.Marvin Ray Burns (talk) 04:19, 4 February 2015 (UTC) Mathar's paper is essentially about the MRB constant's series (its integral analog anyway). Both him and Crandall have cared to study this number Marvin Ray Burns (talk) 04:29, 4 February 2015 (UTC) Arthur Rubin, can you now at least consider removing the notability tag, please? Or at lest consider merging the MRB constant with an yet to be written article on its integral analog?Marvin Ray Burns (talk) 04:37, 4 February 2015 (UTC)

An article on the class of numbers (iterated exponential constants?) might be appropriate, with an notability criteria related to classes of numbers. If that were written, the MRB constant could be a section of that article, and MRB constant a redirect to that section, and probably 'not listed in list of mathematical constants or mathematical constants (which probably should be merged and resplit on different criteria), and certainly not in list of numbers. List of numbers needs to be significantly trimmed for non-integers, and I suspect even the integer table should be on a WikiProject Mathematics or WikiProject Numbers page, not in article-space. But I digress.

So, no, I don't consider the number notable, and I certainly don't consider the notability criteria applicable to classes of numbers to be applicable to the number recognized as the representative of the type. $\int _{0}^{1}x^{\pm x}\mathrm {d} x$ might be appropriate constants, if they had names. I'm sure I've seen multiple discussions of those integrals, including representations as sums of exponentials. As for the example from the guideline, numbers (not necessarily transcendental, between 0 and 1) containing only 3 and 7 in (their) hexidecimal representation form a generalized Cantor set, and a fractal of dimension ${\frac {\ln 2}{\ln 16}}={\frac {1}{4}}.$ Fractal generalized Cantor sets are a subject of discussion, and even those formed by selecting digits in some base would probably have a number of papers about them, but I don't know of a common name. — Arthur Rubin (talk) 17:50, 4 February 2015 (UTC)

Iterated Exponential Constant

I posted a reward for an article on iterated exponential constants in the Wikipedia:Reward_board. — Preceding unsigned comment added by Marburns (talk • contribs) 01:40, 6 February 2015 (UTC)

another link to the series of the MRB constant with my name!

http://web.archive.org/web/20000412181358/http://www.mathsoft.com/asolve/constant/itrexp/itrexp.html Marvin Ray Burns (talk) 02:35, 6 February 2015 (UTC)

A compromise in the works

I see a potential compromise in the works: In https://wiki.riteme.site/w/index.php?title=Mathematical_constant&action=historyhttps://wiki.riteme.site/w/index.php?title=Mathematical_constant&action=history David Eppstein, said, "Remove MRB — seems notable enough for its own article but not for inclusion in a top-20-constants list)." I am willing to concede that the standard for being on that short list is a little too high for the MRB constant's present notability. I am willing abide by Dr. Eppstein, action, so long as the MRB constant's own article stays. I do think, however, the article needs to be fixed: I would like to see more of what its references say about it (Cradall's two eta formulas and Mathar's convergence rates, for examples) incorporated into the article. Perhaps some lesser notable aspects (like my math binge) could be removed. Marvin Ray Burns (talk) 20:14, 15 February 2015 (UTC)

Notability

I see that this article is still tagged for notability. My bar for notability of mathematical research topics (based on WP:GNG) is pretty low: I want to see published sources by more than one author or group of authors, independent of the creator of the concept, that say something nontrivial about it. In this case we have the MathWorld article and arxiv:0912.3844, for which "published" is a little dubious but they are definitely independent and cover the subject nontrivially. There's also nontrivial coverage in Crandall although it's a much smaller fraction of the overall work. So although I think the primary-sourced "math binge" material can go, and the "low" importance rating in the math project banner is certainly correct, I also think there's enough here to justify an article. —David Eppstein (talk) 22:31, 16 February 2015 (UTC)

Fair enough; that's a reasonable argument. At least the constant's namesake is not solely responsible for its publication, unlike a certain function I could name. I have no objection to withdrawal of the tag, although I am not fully convinced it's notable yet. — Arthur Rubin (talk) 23:57, 16 February 2015 (UTC)

Thank you David Eppstein and Arthur Rubin. Arthur, can I remove the tag or does the person who placed it there have to be the one to remove it? Marvin Ray Burns (talk) 04:56, 17 February 2015 (UTC)

I believe I placed it; if so, you have my permission to remove it. Does that resolve your question. Normally, the tag, if placed properly, can be removed by WP:CONSENSUS, if there is no further discussion, or if, per WP:SNOW, there has been adequate discussion and there are no objections to removal. Once properly removed, it cannot be added unless new concerns are brought, or with WP:CONSENSUS. — Arthur Rubin (talk) 05:30, 17 February 2015 (UTC)

neutral point of view

Per COI tag: as the major contributor to this article who appears to have a close connection with its subject, I would like to say the following to clear matters. Although I thought all edits I made were for the all around advancement of encyclopedic knowledge of this subject and could have been understood as innocent if judged in assuming good faith and using common sense, if I have crossed the line of conflict of interest with any one, or more, specific edit(s), please change or revert that or those specific edits. Marvin Ray Burns (talk) 03:24, 27 February 2016 (UTC) Taking a fresh look at my contribution edits show that they mostly fall into two categories: 1. supplementing material already in the article with references, and 2. adding content that later was undone. 3. undoing a little unintended vandalism. Anything else that I contributed has had a few years to be undone by other editors who have visited. I move that someone should remove the neutral point of view tag. Marvin Ray Burns (talk) 20:19, 25 November 2016 (UTC)

External links modified

Hello fellow Wikipedians,

I have just added archive links to one external link on MRB constant. Please take a moment to review my edit. You may add {{cbignore}} after the link to keep me from modifying it, if I keep adding bad data, but formatting bugs should be reported instead. Alternatively, you can add {{nobots|deny=InternetArchiveBot}} to keep me off the page altogether, but should be used as a last resort. I made the following changes:

• Attempted to fix sourcing for http://www.perfscipress.com/papers/UniversalTOC25.pdf

When you have finished reviewing my changes, please set the checked parameter below to true or failed to let others know (documentation at {{Sourcecheck}}).

This message was posted before February 2018. After February 2018, "External links modified" talk page sections are no longer generated or monitored by InternetArchiveBot. No special action is required regarding these talk page notices, other than regular verification using the archive tool instructions below. Editors have permission to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the RfC before doing mass systematic removals. This message is updated dynamically through the template {{source check}} (last update: 5 June 2024).

• If you have discovered URLs which were erroneously considered dead by the bot, you can report them with this tool.
• If you found an error with any archives or the URLs themselves, you can fix them with this tool.

Cheers.—^{cyberbot II}_{Talk to my owner:Online} 04:09, 31 March 2016 (UTC)

Assessment comment

The comment(s) below were originally left at Talk:MRB constant/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.

===Errata and addenda=== ustress We should change footnote 3 to, [3]^ Plouffe, Simon. (1999-11-20). "Tables of Constants". Laboratoire de combinatoire et d'informatique mathématique. http://pi.lacim.uqam.ca/eng/table_en.html. Retrieved on 2009-05-05. Also we can link Simon Plouffe. Thanks. Marvin Ray Burns (talk) 22:55, 7 May 2009 (UTC)

Last edited at 01:38, 1 January 2012 (UTC). Substituted at 02:18, 5 May 2016 (UTC)

Key fundamental constant among polylogarithm, L-series, and zeta variants

At https://web.archive.org/web/20130430193005/http://www.perfscipress.com/papers/UniversalTOC25.pdf , Richard Crandall wrote about Unified algorithms for polylogarithm, L-series, and zeta variants. Since, according to Google Scholar, this paper was cited 8 times in its first year (how much longer he lived), I believe this paper is a suitable source.

When he got to chapter 7, he called it "Key fundamental constants." I searched for the meaning of Key fundamental constants, on google and found it referred to different constants for different applications, Physical, dimensionless, etc.

If the MRB constant is a Key fundamental constant among polylogarithm, L-series, and zeta variants, could someone make a small note saying so in the article? Marvin Ray Burns (talk) 16:33, 18 June 2016 (UTC)

NSF sponsored link to paper that defines and uses MRB constant

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.695.5959&rep=rep1&type=pdf Marvin Ray Burns (talk) 19:54, 26 June 2016 (UTC)

That appears to be a chapter in a self-published book by Richard Crandall. Being collected on an NSF-sponsored web-scraper has nothing to do with it or its reliability. Crandall may be notable enough to pass the "recognized expert" clause of WP:SPS but the case is weak. —David Eppstein (talk) 20:09, 26 June 2016 (UTC)

Another journal-published paper with new analysis of the MRB constant

While searching for anything new on MRB I found the following paper, "On the Asymptotics of Sums Related to the Stieltjes Constants" at http://vixra.org/abs/1608.0375 . Is there anything worthwhile in it to reference in the MRB constant article? Marvin Ray Burns (talk) 01:13, 4 September 2016 (UTC)

Newly published info on the MRB constant

I noticed that http://mathworld.wolfram.com/MRBConstant.html has been updated including a book reference to Crandall, R. E. "The MRB Constant." §7.5 in Algorithmic Reflections: Selected Works. PSI Press, pp. 28-29, 2012b. Marvin Ray Burns (talk) 00:38, 1 November 2017 (UTC)

Removal of neutral point of view tag

I think the neutral point of view issue has been fully addressed. Seeing, i may not remove it for a conflict of interest issue being started all over again! If anyone else thinks the issue has been resolved, could you see fit to remove the tag?Marvin Ray Burns (talk) 14:52, 26 April 2019 (UTC)

Done. Jamgoodman (talk) 22:14, 29 April 2019 (UTC)

The MRB constant used as a sample of e convergent series and sequences attained from the convergent half-life related series.

For consideration in the article: http://www.ccsenet.org/journal/index.php/jmr/article/view/0/41147

Marvin Ray Burns (talk) 08:10, 21 January 2020 (UTC)

Abel-Plana formula.

For consideration in the article: In Mathematics in the Stack Exchange Network, an internet scholar going by the moniker Dark Malthorp presented a beautiful integral for the MRB constant: the integral of Im[(1 + I t)^(1/(1 + I t))]/Sinh[Pi t] for t>0. See What are some working models that are fit the formula for the MRB constant?

Marvin Ray Burns (talk) 08:13, 21 January 2020 (UTC)

Key fundamental constant among polylogarithm, L-series, and zeta variants

For consideration in the article: At http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.695.5959&rep=rep1&type=pdf , Richard Crandall wrote about Unified algorithms for polylogarithm, L-series, and Zeta variants. Marvin Ray Burns (talk) 11:37, 21 January 2020 (UTC)

COI by Marburns on external sites

On Quora (Quora Question). I was asked to answer a question related to this page and a question on the Reward Board. It clearly seems to by MRB trying to influence the page via other means.

I've added a note of a connected contributor above. This all seems to push WP:COI to the limits. --Salix alba (talk): 17:04, 5 June 2021 (UTC)

I believe there are reliable sources that aren't being used on the page, as I mentioned on this talk page. Perhaps, I am too impatient. I will delete the Quora "Can-you-add-reliable-sources-to-this-Wikipedia-article?" request, which simply said, "Can you add reliable sources to this Wikipedia article?" and wait and see if the reward board request alone brings any new sources to the article.Marvin Ray Burns (talk) 22:54, 5 June 2021 (UTC)

Actually, I don't see how to delete the Quora question. I already decided not to request any more answers (responses), so I guess it will stand as a record of my impatience.Marvin Ray Burns (talk) 23:05, 5 June 2021 (UTC)

conversation with https://chat.openai.com/chat

I just thought the following, where I cut and pasted Math world's and Wikipedia's articles into Open AI, could give an editor some ideas if they thought this article could use an update:

I entered:

Rewrite the following for Wikipedia:

Then I cut and pasted Wikipedia's and Wolfram MathWorld's articles.

The MRB constant is a mathematical constant that is the upper limit point of a sequence of partial sums. The sequence is defined by the sum of alternating powers of positive integers raised to the power of their reciprocal, and is given by the expression:

s_n = sum_(k=1)^n (-1)^k k^(1/k)

The MRB constant is equal to 0.1878596424..., and can also be represented as a sum over derivatives of the Dirichlet eta function or as an integral expression involving the inverse hyperbolic cosecant and a certain inverse power. No closed-form expression for the constant is currently known. The constant was first investigated by M.R. Burns in 1999 and was named after his initials.

The MRB constant has connections to several areas of mathematics, including number theory, probability and statistics, and recreational mathematics. It is listed in mathematical reference works and is available for exploration and computation through Wolfram Alpha and Mathematica.

References:

Burns, M. R. "An Alternating Series Involving n^(th) Roots." Unpublished note, 1999.

Burns, M. R. "Try to Beat These MRB Constant Records!" http://community.wolfram.com/groups/-/m/t/366628.

Crandall, R. E. "Unified Algorithms for Polylogarithm, L-Series, and Zeta Variants." 2012a. http://www.marvinrayburns.com/UniversalTOC25.pdf.

Crandall, R. E. "The MRB Constant." §7.5 in Algorithmic Reflections: Selected Works. PSI Press, pp. 28-29, 2012b.

Finch, S. R. Mathematical Constants. Cambridge, England: Cambridge University Press, p. 450, 2003.

Plouffe, S. "MRB Constant." http://pi.lacim.uqam.ca/piDATA/mrburns.txt.

Sloane, N. J. A. Sequences A037077 in "The On-Line Encyclopedia of Integer Sequences."

Marvin Ray Burns (talk) 15:20, 4 February 2023 (UTC)

Marvin Ray Burns (talk) 10:01, 5 February 2023 (UTC)