OFFSET
0,1
LINKS
M. L. Glasser, A note on Beukers's and related integrals, Amer. Math. Monthly 126(4) (2019), 361-363.
Eric Weisstein's World of Mathematics, Sophomore's Dream.
FORMULA
Equals (1/2)*Integral_{x = 0..1} 1/x^(x/2) dx.
Equals (-1/2)*Integral_{x = 0..1} log(x)/(x^(x/2)) dx.
Equals the double integral (1/2)*Integral_{x = 0..1, y = 0..1} 1/(x*y)^(x*y/2) dx dy (apply Glasser, Theorem 1).
EXAMPLE
0.5673841148770283225412148375703239748858395078475...
MAPLE
evalf( add( 1/(2*n)^n, n = 1..50), 100);
PROG
(PARI) suminf(n=1, 1/(2*n)^n) \\ Michel Marcus, Nov 03 2022
CROSSREFS
KEYWORD
AUTHOR
Peter Bala, Nov 03 2022
STATUS
approved