A193713 - OEIS

%I #23 Apr 22 2023 18:18:27

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

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

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

%N Decimal expansion of 11*Pi^5/1440.

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

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

%C The value of Pi/2*(d^2/db^2(d^2/da^2(gamma(b+1)/gamma((b+a)/2+1)/gamma((b-a)/2+1)))) at a=0 and b=0. [_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

%H Jonathan Sondow and Eric W. Weisstein <a href="http://mathworld.wolfram.com/HarmonicNumber.html">Harmonic Number</a> (22)

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%F Equals 11*A092731/1440.

%e 2.3376503698875666568...

%t RealDigits[ N[11 Pi^5/1440, 150]][[1]]

%Y Cf. A152584, A193712, A194655.

%K cons,easy,nonn

%O 1,1

%A _Seiichi Kirikami_, Aug 31 2011