- Definition
- History
- References
- External links
The MRB constant, named after Marvin Ray Burns, is a mathematical constant for which no closed-form expression is known. It is not known whether the MRB constant is algebraic, transcendental, or even irrational.
The numerical value of MRB constant, truncated to 6 decimal places, is
{{nowrap|0.187859…}} {{OEIS|A037077}}.
Definition
The MRB constant is related to the following divergent series:
Its partial sums
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 known as the MRB constant.[1][1][2][3][4][5][6]
The MRB constant can be explicitly defined by the following infinite sums:[7]
There is no known closed-form expression of the MRB constant.[8]
History
Marvin Ray Burns published his discovery of the constant in 1999.[9] The discovery is a result of a "math binge" that started in the spring of 1994.[10] 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.[11] At Plouffe's suggestion, the constant was renamed Marvin Ray Burns's Constant, and then shortened to "MRB constant" in 1999.[12]
References
2. ^{{cite web |last=Crandall |first=Richard |title=Unified algorithms for polylogarithm, L-series, and zeta variants |url=http://www.perfscipress.com/papers/UniversalTOC25.pdf |publisher=PSI Press |accessdate=16 January 2015 |deadurl=yes |archiveurl=https://web.archive.org/web/20130430193005/http://www.perfscipress.com/papers/UniversalTOC25.pdf |archivedate=April 30, 2013}}
3. ^{{OEIS|id=A037077}}
4. ^{{OEIS|id=A160755}}
5. ^{{OEIS|id=A173273}}
6. ^{{cite web |last=Fiorentini |first=Mauro |title=MRB (costante) |url=http://www.bitman.name/math/article/962 |website=bitman.name |accessdate=14 January 2015 |language=italian}}
7. ^1 {{MathWorld |title=MRB Constant |urlname=MRBConstant}}
8. ^{{cite book |title=Mathematical Constants |last=Finch |first=Steven R. |year=2003 |publisher=Cambridge University Press |location=Cambridge, England |isbn=0-521-81805-2 |page=450}}
9. ^{{cite web |last=Plouffe|first=Simon|title=mrburns |url=http://www.plouffe.fr/simon/constants/mrburns.txt|accessdate=12 January 2015}}
10. ^{{cite web |last=Burns |first=Marvin R. |title=Captivity's Captor: Now is the Time for the Chorus of Conversion |url=https://oncourse.iu.edu/access/content/user/marburns/Filemanager_Public_Files/final1.doc |date=12 April 2002 |publisher=Indiana University |accessdate=5 May 2009}}
11. ^{{cite web |last=Burns |first=Marvin R. |title=RC |url=http://math2.org/mmb/thread/901 |date=23 January 1999 |website=math2.org |accessdate=5 May 2009}}
12. ^{{cite web |last=Plouffe |first=Simon |title=Tables of Constants |url=http://www.plouffe.fr/simon/articles/Tableofconstants.pdf |date=20 November 1999 | publisher=Laboratoire de combinatoire et d'informatique mathématique |accessdate=5 May 2009}}
External links
{{Portal|Mathematics}}- Official site of M.R. Burns, constant's author
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