OFFSET
1,1
COMMENTS
The value of the integral_{x=0..Pi/2} log(sin(x))^2 dx. The value of sqrt(Pi)/2*(d^2/da^2(gamma((a+1)/2)/gamma(a/2+1))) at a=0. - Seiichi Kirikami and Peter J. C. Moses, Oct 07 2011
REFERENCES
I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, 4th edition, 3.621.1
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..10000
K. S. Kolbig, On the integral int_0^Pi/2 log^n cos x log^p sin x dx, Math. Comp. 40 (162) (1983) 565-570, r_{2,0}
FORMULA
Equals Integral_{x=0..1} log(x)^2/sqrt(1-x^2) dx. - Amiram Eldar, May 27 2023
EXAMPLE
2.04662202447274064616964100817...
MATHEMATICA
RealDigits[N[Pi/2 (Pi^2/12 + Log[2]^2), 150] [[1]]
PROG
(PARI) Pi/2*(Pi^2/12+(log(2))^2) \\ Michel Marcus, Jan 13 2015
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Seiichi Kirikami, Oct 07 2011
STATUS
approved