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A157852
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Absolute value of limit_{N -> infinity} integral((-1)^x*x^(1/x),x=1..2*N).
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2
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6, 8, 7, 6, 5, 2, 3, 6, 8, 9, 2, 7, 6, 9, 4, 3, 6, 9
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| The continuous counterpart of 1^(1/1)-2^(1/2)+3^(1/3)-4^(1/4)...2*integer as n->infinity.
It is hard to integrate and very slow to converge.
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LINKS
| M. R. Burns, Used with other constants to converge closely to rational numbers.
M. R. Burns, Author's public inquiry 1
M. R. Burns, Author's public inquiry 2
R. J. Mathar, Numerical evaluation of the oscillatory integral over exp(i*pi*x)x^(1/x) between 1 and infinity, arxiv:0912.3844 [math.CA] [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 21 2010]
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EXAMPLE
| After integrating from 1 to 15 Million the absolute value of the integral is approximately 0.6876527177, after integrating from 1 to 20 Million approximately 0.6876526145.
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CROSSREFS
| Integrating A037077 instead of summing.
Sequence in context: A092294 A097668 A133748 * A088608 A176104 A011481
Adjacent sequences: A157849 A157850 A157851 * A157853 A157854 A157855
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KEYWORD
| nonn,cons,more
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AUTHOR
| Marvin Ray Burns (bmmmburns(AT)sbcglobal.net), Mar 07 2009, Mar 11 2009, Mar 13 2009
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EXTENSIONS
| Edited by N. J. A. Sloane, Mar 13 2009
Corrected and edited by Marvin Ray Burns (bmmmburns(AT)sbcglobal.net), Apr 03 2009
8 more digits from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 30 2009
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