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A083648 Decimal expansion of Sum_{n=1..Infinity} -(-1)^n/n^n = Integral_{x=0..1} x^x dx. 10
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; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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.

REFERENCES

William Dunham, The Calculus Gallery, Masterpieces from Newton to Lebesgue, Princeton University Press, Princeton, NJ 2005, page 46-51.

Paul J. Nahin, An Imaginary Tale: The Story of sqrt(-1), Princeton, New Jersey: Princeton University Press (1988) page 146.

LINKS

Table of n, a(n) for n=0..104.

Eric Weisstein's World of Mathematics, Power Tower

Eric Weisstein's World of Mathematics, Sophomore's Dream

FORMULA

Constant also equals the double integral int {y = 0..1} int {x = 0..1} (x*y)^(x*y) dx dy. - Peter Bala, Mar 04 2012

EXAMPLE

0.78343051071213440705926438652697546940768199014693095825541782270...

MATHEMATICA

RealDigits[ Sum[ -(-1)^n /n^n, {n, 1, 60}], 10, 111] [[1]] (* Robert G. Wilson v, Jan 31 2005 *)

PROG

(PARI) -sumalt(n=1, (-1/n)^(n)) \\ Michel Marcus, Oct 15 2015

CROSSREFS

Cf. A073009. The minimum point on the curve x^x is (A068985, A072364).

Sequence in context: A064207 A020843 A241296 * A133613 A194622 A193010

Adjacent sequences:  A083645 A083646 A083647 * A083649 A083650 A083651

KEYWORD

cons,nonn

AUTHOR

Eric W. Weisstein, May 01 2003

STATUS

approved

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Last modified December 9 14:38 EST 2016. Contains 278971 sequences.