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A358203 Decimal expansion of Sum_{n >= 1} 1/(2*n)^n.

%I A358203 #11 Feb 16 2025 08:34:04
%S A358203 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,
%T A358203 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,
%U A358203 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
%N A358203 Decimal expansion of Sum_{n >= 1} 1/(2*n)^n.
%H A358203 M. L. Glasser, <a href="https://doi.org/10.1080/00029890.2019.1565856">A note on Beukers's and related integrals</a>, Amer. Math. Monthly 126(4) (2019), 361-363.
%H A358203 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SophomoresDream.html">Sophomore's Dream</a>.
%F A358203 Equals (1/2)*Integral_{x = 0..1} 1/x^(x/2) dx.
%F A358203 Equals (-1/2)*Integral_{x = 0..1} log(x)/(x^(x/2)) dx.
%F A358203 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).
%e A358203 0.5673841148770283225412148375703239748858395078475...
%p A358203 evalf( add( 1/(2*n)^n, n = 1..50), 100);
%o A358203 (PARI) suminf(n=1, 1/(2*n)^n) \\ _Michel Marcus_, Nov 03 2022
%Y A358203 Cf. A073009, A098686, A358191, A358204.
%K A358203 cons,nonn,easy
%O A358203 0,1
%A A358203 _Peter Bala_, Nov 03 2022