A359283 - OEIS

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

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OFFSET

0,1

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.

LINKS

Table of n, a(n) for n=0..100.

Peter Bala, Borel summation of a family of divergent series

Wikipedia, Sophomore's Dream

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.

EXAMPLE

0.46230371153732107718203962858827744096102603704840...

MAPLE

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

MATHEMATICA

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

CROSSREFS

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

Sequence in context: A286155 A195860 A106143 * A255524 A077158 A059854

Adjacent sequences: A359280 A359281 A359282 * A359284 A359285 A359286

KEYWORD

nonn,cons,easy

AUTHOR

Peter Bala, Dec 24 2022

STATUS

approved