OFFSET
0,1
COMMENTS
The absolute value of Integral_{x=0..Pi/2} x^2*log(2*cos(x)) dx.
The absolute value of (d/db(d^2/da^2(Integral_{x=0..Pi/2} cos(ax)*(2*cos(x))^b dx))).
The absolute value of (Pi/2)*(d/db(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
Masato Kobayashi, Integral representations for zeta(3) with the inverse sine function, arXiv:2108.01247 [math.NT], 2021.
FORMULA
Equals 2 * Integral_{x=0..1} arcsin(x)^2*arccos(x)/x dx (Kobayashi, 2021). - Amiram Eldar, Jun 23 2023
EXAMPLE
0.94409328404076973180...
MATHEMATICA
RealDigits[ N[Pi Zeta[3]/4, 150]][[1]]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Seiichi Kirikami, Aug 31 2011
STATUS
approved