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Decimal expansion of log(2)/3 + zeta(3)/(2*Pi^2).
0

%I #12 Aug 19 2024 03:13:15

%S 2,9,1,9,4,5,9,7,4,3,0,3,4,3,4,9,7,8,0,3,2,9,1,3,7,6,8,0,9,5,0,3,5,0,

%T 7,5,9,8,5,8,3,4,3,4,5,2,1,0,0,3,2,9,5,7,2,1,2,8,3,7,1,1,6,2,1,5,8,7,

%U 3,5,0,9,8,7,9,7,7,2,0,3,5,8,9,0,8,7,6,9

%N Decimal expansion of log(2)/3 + zeta(3)/(2*Pi^2).

%H Olivier Espinosa and Victor H. Moll, <a href="https://dx.doi.org/10.1023/A:1015706300169">On some integrals involving the Hurwitz zeta function: Part 1</a>, Raman. J. 6 (2002) 159-188, eq. (5.7).

%F Equals -Integral_{x=0..1} x^2* log(sin(Pi*x)) dx.

%e 0.29194597430343497803291376809503507598583434521003...

%p log(2)/3+Zeta(3)/2/Pi^2 ; evalf(%) ;

%t RealDigits[Log[2] / 3 + Zeta[3] / (2*Pi^2), 10, 120][[1]] (* _Amiram Eldar_, Aug 19 2024 *)

%Y Cf. A193535.

%K nonn,cons

%O 0,1

%A _R. J. Mathar_, Aug 13 2024