OFFSET
1,1
COMMENTS
The absolute value of Integral_{x=0..Pi/2} x^2*(log(2*cos(x)))^3 dx.
The absolute value of d^3/db^3(d^2/da^2(Integral_{x=0..Pi/2} cos(ax)*(2*cos(x))^b dx))).
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]
REFERENCES
I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, 4th edition, 3.631.9
EXAMPLE
Equals 7.1021170790001686158...
MATHEMATICA
RealDigits[ N[Pi (Pi^2*Zeta(3)+6*Zeta(5))/8, 150]][[1]]
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Seiichi Kirikami, Aug 31 2011
STATUS
approved