A359283 - OEIS

%I #13 Dec 27 2022 16:53:55

%S 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,

%T 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,

%U 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

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

%C 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.

%H Peter Bala, <a href="/A245637/a245637.pdf">Borel summation of a family of divergent series</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Sophomore%27s_dream">Sophomore's Dream</a>

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

%F 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.

%e 0.46230371153732107718203962858827744096102603704840...

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

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

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

%K nonn,cons,easy

%O 0,1

%A _Peter Bala_, Dec 24 2022