A194655 - OEIS

%I #25 Apr 03 2023 05:33:57

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

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

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

%N Decimal expansion of Pi*(Pi^2*zeta(3) + 6*zeta(5))/8.

%C The absolute value of Integral_{x=0..Pi/2} x^2*(log(2*cos(x)))^3 dx.

%C The absolute value of d^3/db^3(d^2/da^2(Integral_{x=0..Pi/2} cos(ax)*(2*cos(x))^b dx))).

%C The absolute value of m=2 and n=3 of (Pi/2)*(d^n/db^n(d^m/da^m(gamma(b+1)/gamma((b+a)/2+1)/gamma((b-a)/2+1)))). [_Seiichi Kirikami_ and _Peter J. C. Moses_]

%D I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, 4th edition, 3.631.9

%F Equals A000796*(A002388*A002117 + 6*A013663)/8.

%e Equals 7.1021170790001686158...

%t RealDigits[ N[Pi (Pi^2*Zeta(3)+6*Zeta(5))/8, 150]][[1]]

%Y Cf. A152584, A193712, A193713, A194655.

%K cons,nonn

%O 1,1

%A _Seiichi Kirikami_, Aug 31 2011