A377645 - OEIS

%I #5 Nov 04 2024 01:48:16

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

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

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

%N Decimal expansion of 2*Pi^2*log(2) - 7*zeta(3).

%D Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.6.5, p. 46.

%H Michael I. Shamos, <a href="http://euro.ecom.cmu.edu/people/faculty/mshamos/cat.pdf">A catalog of the real numbers</a>, (2007). See p. 305.

%F Equals -4*Integral_{x=0..Pi} x*log(sin(x/2)) dx = 8*Integral_{x=0..1} arcsin(x)^2/x dx = 8*Integral_{x=0..Pi/2} x^2*cot(x) dx (see Finch).

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

%e 5.26777860559707309189679117732804220724465404999...

%t RealDigits[2Pi^2Log[2]-7Zeta[3],10,100][[1]]

%Y Cf. A002117, A002162, A002388, A016627, A164102.

%K nonn,cons

%O 1,1

%A _Stefano Spezia_, Nov 03 2024