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} 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} (x*y)^(x*y/2) dx dy (apply Glasser, Theorem 1).
EXAMPLE
0.44189516336521830719032130562070863787479928...
MAPLE
evalf( add( (-1)^(n+1)/(2*n)^n, n = 1..50), 100);
MATHEMATICA
RealDigits[N[Integrate[x^(x/2), {x, 0, 1}]/2, 120]][[1]] (* Amiram Eldar, Jun 21 2023 *)
PROG
(PARI) suminf(n=1, (-1)^(n+1)/(2*n)^n) \\ Michel Marcus, Nov 03 2022
CROSSREFS
KEYWORD
AUTHOR
Peter Bala, Nov 03 2022
EXTENSIONS
a(98)-a(99) corrected by Amiram Eldar, Jun 21 2023
STATUS
approved