OFFSET
1,1
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
Peter Bala, Borel summation of a family of divergent series
Wikipedia, Sophomore's Dream
FORMULA
Equals Integral_{x = 1..oo} 1/(3*x - 2)^x dx.
Equals the Borel sum of the alternating divergent series Sum_{n >= 0} (-1)^n*(3*n + 2)^n. Compare with the alternating convergent series Sum_{n >= 1} (-1)^(n+1)/(3*n - 2)^n = Integral_{x = 0..1} x^(x^3) dx. See A359285.
EXAMPLE
0.35854271600033996570705760779181131168203620572130...
MAPLE
evalf(int(1/x^(x^3), x = 1..infinity), 110);
MATHEMATICA
NIntegrate[1/x^(x^3), {x, 1, Infinity}, WorkingPrecision -> 110] // RealDigits // First
CROSSREFS
KEYWORD
AUTHOR
Peter Bala, Dec 24 2022
STATUS
approved