OFFSET
1,1
COMMENTS
The value of Integral_{x=0..Pi/2} x^2*(log(2*cos(x)))^2 dx.
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.
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]
REFERENCES
I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, 4th edition, 3.631.9
LINKS
Jonathan Sondow and Eric W. Weisstein Harmonic Number (22)
FORMULA
Equals 11*A092731/1440.
EXAMPLE
2.3376503698875666568...
MATHEMATICA
RealDigits[ N[11 Pi^5/1440, 150]][[1]]
CROSSREFS
KEYWORD
AUTHOR
Seiichi Kirikami, Aug 31 2011
STATUS
approved