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A358203
Decimal expansion of Sum_{n >= 1} 1/(2*n)^n.
1
5, 6, 7, 3, 8, 4, 1, 1, 4, 8, 7, 7, 0, 2, 8, 3, 2, 2, 5, 4, 1, 2, 1, 4, 8, 3, 7, 5, 7, 0, 3, 2, 3, 9, 7, 4, 8, 8, 5, 8, 3, 9, 5, 0, 7, 8, 4, 7, 5, 4, 7, 1, 8, 0, 2, 1, 0, 0, 5, 5, 1, 4, 8, 7, 3, 7, 3, 0, 2, 5, 2, 8, 2, 5, 2, 4, 0, 5, 8, 8, 5, 8, 8, 4, 8, 2, 2, 1, 3, 2, 5, 8, 0, 1, 5, 7, 4, 5, 6, 8
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
cons,nonn,easy
AUTHOR
Peter Bala, Nov 03 2022
STATUS
approved