MRB constant: Difference between revisions
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Its [[partial sum]]s |
Its [[partial sum]]s |
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: <math>s_n = \sum_{k=1}^n (-1)^k k^{1/k}</math> |
: <math>s_n = \sum_{k=1}^n (-1)^k k^{1/k}</math> |
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are bounded so that their [[limit point]]s form an [[interval (mathematics)|interval]] [−0.812140…,0.187859…] of length 1. The [[upper limit]] point 0.187859… is what is known as the MRB constant.<ref>{{cite web|last1=Weisstein|first1=Eric W|title="MRB Constant.|url=http://mathworld.wolfram.com/MRBConstant.html|website=MathWorld|publisher=MathWorld--A Wolfram Web Resource|accessdate=12 January 2015}}</ref><ref>{{cite web|last1=MATHAR|first1=RICHARD J|title=NUMERICAL EVALUATION OF THE OSCILLATORY INTEGRAL OVER exp(iπx) x^*1/x) BETWEEN 1 AND INFINITY|url=http://arxiv.org/pdf/0912.3844v3.pdf|website=arxiv|publisher=Cornell University|accessdate=12 January 2015}}</ref><ref>{{cite web|last1=Crandall|first1=Richard|title=Unified algorithms for polylogarithm, L-series, and zeta variants|url=http://web.archive.org/web/20130430193005/http://www.perfscipress.com/papers/UniversalTOC25.pdf|website=http://web.archive.org/|publisher=PSI Press|accessdate=16 January 2015}}</ref><ref>{{OEIS|id=A037077}}</ref><ref>{{OEIS|id=A160755}}</ref><ref> {{OEIS|id=A173273}}</ref> |
are bounded so that their [[limit point]]s form an [[interval (mathematics)|interval]] [−0.812140…,0.187859…] of length 1. The [[upper limit]] point 0.187859… is what is known as the MRB constant.<ref>{{cite web|last1=Weisstein|first1=Eric W|title="MRB Constant.|url=http://mathworld.wolfram.com/MRBConstant.html|website=MathWorld|publisher=MathWorld--A Wolfram Web Resource|accessdate=12 January 2015}}</ref><ref>{{cite web|last1=MATHAR|first1=RICHARD J|title=NUMERICAL EVALUATION OF THE OSCILLATORY INTEGRAL OVER exp(iπx) x^*1/x) BETWEEN 1 AND INFINITY|url=http://arxiv.org/pdf/0912.3844v3.pdf|website=arxiv|publisher=Cornell University|accessdate=12 January 2015}}</ref><ref>{{cite web|last1=Crandall|first1=Richard|title=Unified algorithms for polylogarithm, L-series, and zeta variants|url=http://web.archive.org/web/20130430193005/http://www.perfscipress.com/papers/UniversalTOC25.pdf|website=http://web.archive.org/|publisher=PSI Press|accessdate=16 January 2015}}</ref><ref>{{OEIS|id=A037077}}</ref><ref>{{OEIS|id=A160755}}</ref><ref> {{OEIS|id=A173273}}</ref><ref>{{cite web|last1=Fiorentini|first1=Mauro|title=MRB (costante)|url=http://www.bitman.name/math/article/962|website=bitman.name|publisher=Mauro Fiorentini|accessdate=14 January 2015|language=italian}}</ref> |
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The MRB constant can be explicitly defined by the following infinite sums:<ref name="Weisstein">{{MathWorld|title=MRB Constant|urlname=MRBConstant}}</ref> |
The MRB constant can be explicitly defined by the following infinite sums:<ref name="Weisstein">{{MathWorld|title=MRB Constant|urlname=MRBConstant}}</ref> |
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Revision as of 00:27, 29 January 2015
 | The topic of this article may not meet Wikipedia's general notability guideline. (January 2015) |
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
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][2][3][4][5][6][7]
The MRB constant can be explicitly defined by the following infinite sums:[8]
There is no known closed-form expression of the MRB constant.[9]
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.[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
- ^ Weisstein, Eric W. ""MRB Constant". MathWorld. MathWorld--A Wolfram Web Resource. Retrieved 12 January 2015.
- ^ MATHAR, RICHARD J. "NUMERICAL EVALUATION OF THE OSCILLATORY INTEGRAL OVER exp(iπx) x^*1/x) BETWEEN 1 AND INFINITY" (PDF). arxiv. Cornell University. Retrieved 12 January 2015.
- ^ Crandall, Richard. "Unified algorithms for polylogarithm, L-series, and zeta variants" (PDF). http://web.archive.org/. PSI Press. Retrieved 16 January 2015.
{{cite web}}: External link in|website= - ^ (sequence A037077 in the OEIS)
- ^ (sequence A160755 in the OEIS)
- ^ (sequence A173273 in the OEIS)
- ^ Fiorentini, Mauro. "MRB (costante)". bitman.name (in Italian). Mauro Fiorentini. Retrieved 14 January 2015.
- ^ Weisstein, Eric W. "MRB Constant". MathWorld.
- ^ Finch, Steven R. (2003). Mathematical Constants. Cambridge, England: Cambridge University Press. p. 450. ISBN 0-521-81805-2.
{{cite book}}: Cite has empty unknown parameter:|coauthors=(help) - ^ Burns, Marvin R. (2002-04-12). "Captivity's Captor: Now is the Time for the Chorus of Conversion". Indiana University. Retrieved 2009-05-05.
{{cite web}}: Cite has empty unknown parameter:|coauthors=(help) - ^ Burns, Marvin R. (1999-01-23). "RC". math2.org. Retrieved 2009-05-05.
{{cite web}}: Cite has empty unknown parameter:|coauthors=(help); External link in|publisher= - ^ Plouffe, Simon (1999-11-20). "Tables of Constants" (PDF). Laboratoire de combinatoire et d'informatique mathématique. Retrieved 2009-05-05.
{{cite web}}: Cite has empty unknown parameter:|coauthors=(help); External link in|publisher=
