OFFSET
0,1
COMMENTS
The limiting difference between the integral and sum of x^(1/x). The limit converges slowly.
LINKS
Daniel Hoyt, Graphical representation of the limit.
Wikipedia, Stieltjes Constants
FORMULA
EXAMPLE
0.5681800123590664525123147265218830744...
PROG
(Python 3)
# Gives 15 correct digits
from mpmath import stieltjes, fac, quad
def limgen(n):
terms = []
for y in range(3, n):
for x in range(y, n):
terms.append((((-1)**y)*stieltjes(x)*(x-(y-1))**(y-2))/(fac(x-(y-2))*fac(y-2)))
return terms
f = lambda x: x**(1/x)
int01 = quad(f, [0, 1])
limit = sum(limgen(60)) + 1.5 - stieltjes(0) - int01
print(limit)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Daniel Hoyt, Feb 23 2022
STATUS
approved