A359283 Decimal expansion of Integral_{x = 1..oo} 1/x^(x^2) dx.

4, 6, 2, 3, 0, 3, 7, 1, 1, 5, 3, 7, 3, 2, 1, 0, 7, 7, 1, 8, 2, 0, 3, 9, 6, 2, 8, 5, 8, 8, 2, 7, 7, 4, 4, 0, 9, 6, 1, 0, 2, 6, 0, 3, 7, 0, 4, 8, 4, 0, 7, 5, 6, 2, 2, 7, 0, 1, 3, 0, 0, 6, 0, 2, 5, 6, 7, 8, 2, 3, 3, 7, 7, 0, 2, 4, 0, 9, 8, 4, 4, 7, 7, 3, 4, 1, 7, 5, 4, 6, 1, 0, 5, 4, 2, 3, 3, 8, 6, 1, 8

Offset: 0

Author

Peter Bala, Dec 24 2022

Keywords

• nonn
• cons
• easy

Comments

For a, b nonnegative integers, the alternating divergent series Sum_{n >= 0} (-1)^n*(a*n + b)^n is Borel summable to Integral_{x = 1..oo} x^(a-b-1)/x^(x^a) dx.

Examples

			0.46230371153732107718203962858827744096102603704840...
		

Links

• Peter Bala, Borel summation of a family of divergent series
• Wikipedia, Sophomore's Dream

Crossrefs

Cf. A245637, A253299, A359282, A359284, A359285, A359286.

Programs

Maple

evalf(int(1/x^(x^2), x = 1..infinity), 100);

Mathematica

NIntegrate[1/x^(x^2), {x, 1, Infinity}, WorkingPrecision -> 105] // RealDigits // First

Formula

Equals Integral_{x = 1..oo} 1/(2*x - 1)^x dx.

Equals the Borel sum of the alternating divergent series Sum_{n >= 0} (-1)^n*(2*n + 1)^n. Compare with the alternating convergent series Sum_{n >= 1} (-1)^(n+1)/(2*n - 1)^n = Integral_{x = 0..1} x^(x^2) dx. See A253299.