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A209059 Decimal expansion of the triple integral int {z = 0..1} int {y = 0..1} int {x = 0..1} (x*y*z)^(x*y*z) dx dy dz. 1
8, 3, 4, 9, 3, 0, 1, 1, 0, 6, 3, 6, 2, 2, 3, 5, 9, 3, 5, 1, 0, 3, 3, 8, 6, 9, 0, 7, 7, 8, 2, 2, 1, 6, 6, 0, 2, 8, 6, 6, 0, 3, 2, 2, 5, 0, 1, 2, 2, 4, 4, 3, 5, 5, 1, 3, 7, 4, 7, 8, 3, 9, 9, 2, 0, 8, 3, 5, 7, 6, 6, 5, 2, 3, 9, 4, 5, 6, 4, 1, 1, 2, 1, 2, 8, 1, 9, 4, 4, 8, 6, 3, 2, 4, 5, 6, 8, 9, 2, 7, 0, 0, 6 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The double integral int {y = 0..1} int {x = 0..1} (x*y)^(x*y) dx dy equals int {x = 0..1} x^x dx, which is listed as A083648.

LINKS

Table of n, a(n) for n=0..102.

FORMULA

The triple integral is most conveniently estimated from the identity int {z = 0..1} int {y = 0..1} int {z = 0..1} (x*y*z)^(x*y*z) dx dy dz = 1/2*sum {n = 1..inf} (-1)^(n+1)*(1/n^n + 1/n^(n+1)).

EXAMPLE

0.83493011063622359351...

MATHEMATICA

digits = 103; 1/2*NSum[ (-1)^(n+1)*(1/n^n + 1/n^(n+1)), {n, 1, Infinity}, WorkingPrecision -> digits+10, NSumTerms -> 100] // RealDigits[#, 10, digits]& // First (* Jean-Fran├žois Alcover, Feb 15 2013, from formula *)

CROSSREFS

Cf. A073009, A083648, A209060.

Sequence in context: A014549 A021549 A013665 * A202779 A199440 A199293

Adjacent sequences:  A209056 A209057 A209058 * A209060 A209061 A209062

KEYWORD

nonn,easy,cons

AUTHOR

Peter Bala, Mar 04 2012

STATUS

approved

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Last modified October 20 08:16 EDT 2019. Contains 328253 sequences. (Running on oeis4.)