OFFSET
3,3
LINKS
Jonathan M. Borwein, Armin Straub, Special Values of Generalized Log-sine Integrals.
FORMULA
-Integral_{0..Pi} log(2*sin(t/2))^5 dx = (45/2)*Pi*zeta(5) + (5/4)*Pi^3*zeta(3).
Also equals 5th derivative of -Pi*binomial(x, x/2) at x=0.
EXAMPLE
119.8852400579281896736967018589288678430302320347399435542106179...
MATHEMATICA
RealDigits[(45/2)*Pi*Zeta[5] + (5/4)*Pi^3*Zeta[3], 10, 105] // First
CROSSREFS
KEYWORD
AUTHOR
Jean-François Alcover, Jun 09 2015
STATUS
approved