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Search: id:A083648
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| A083648 |
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Decimal expansion of Sum_{n=1..Infinity} -(-1)^n/n^n = Integral_{x=0..1} x^x dx. |
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+0
5
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| 7, 8, 3, 4, 3, 0, 5, 1, 0, 7, 1, 2, 1, 3, 4, 4, 0, 7, 0, 5, 9, 2, 6, 4, 3, 8, 6, 5, 2, 6, 9, 7, 5, 4, 6, 9, 4, 0, 7, 6, 8, 1, 9, 9, 0, 1, 4, 6, 9, 3, 0, 9, 5, 8, 2, 5, 5, 4, 1, 7, 8, 2, 2, 7, 0, 1, 6, 0, 0, 1, 8, 4, 5, 8, 9, 1, 4, 0, 4, 4, 5, 6, 2, 4, 8, 6, 4, 2, 0, 4, 9, 7, 2, 2, 6, 8, 9, 3, 8, 9, 7, 4, 8, 0, 0
(list; cons; graph; listen)
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OFFSET
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0,1
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COMMENT
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In 1697, Johann Bernoulli explores this curve and finds its minimum and the area under the curve from 0 to 1, all this without the benefit of the exponential function.
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REFERENCES
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William Dunham, The Calculus Gallery, Masterpieces from Newton to Lebesgue, Princeton University Press, Princeton, NJ 2005, page 46-51.
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LINKS
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Eric Weisstein's World of Mathematics, Power Tower
Eric Weisstein's World of Mathematics, Sophomore's Dream
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EXAMPLE
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0.78343051071213440705926438652697546940768199014693095825541782270...
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MATHEMATICA
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RealDigits[ Sum[ -(-1)^n /n^n, {n, 1, 60}], 10, 111] [[1]] (from Robert G. Wilson v Jan 31 2005)
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CROSSREFS
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Cf. A073009. The minimum point on the curve x^x is (A068985, A072364).
Sequence in context: A011103 A064207 A020843 this_sequence A133613 A079082 A091683
Adjacent sequences: A083645 A083646 A083647 this_sequence A083649 A083650 A083651
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KEYWORD
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cons,nonn
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com), May 01, 2003
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