A253299 Decimal expansion of integral_{x=0..1} x^(x^2) dx.
8, 9, 6, 4, 8, 8, 7, 8, 1, 9, 2, 9, 6, 2, 3, 3, 4, 1, 3, 0, 0, 2, 3, 8, 5, 2, 0, 7, 9, 2, 5, 5, 0, 3, 6, 5, 9, 1, 8, 6, 2, 5, 0, 4, 6, 1, 9, 5, 3, 8, 1, 0, 3, 6, 6, 5, 6, 1, 9, 3, 9, 7, 2, 8, 7, 3, 5, 9, 5, 8, 8, 9, 0, 8, 1, 9, 1, 5, 8, 0, 4, 5, 9, 6, 7, 5, 4, 8, 3, 0, 7, 1, 7, 0, 1, 5, 3, 6, 6, 0, 8, 6, 6
Offset: 0
Examples
0.896488781929623341300238520792550365918625...
References
- Paul J. Nahin, Inside Interesting Integrals, Springer 2014, ISBN 978-1493912766.
Links
- Paul J. Nahin, Inside interesting integrals, Undergrad. Lecture Notes in Physics, Springer (2020), (6.1.5)
Programs
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Mathematica
NIntegrate[x^(x^2), {x, 0, 1}, WorkingPrecision -> 103] // RealDigits // First -
PARI
intnum(x=0,1, x^(x^2)) \\ Michel Marcus, Dec 30 2014
Formula
Equals sum_{n >= 0} (-1)^n/(2n + 1)^(n + 1).