OFFSET
4,1
LINKS
Jonathan M. Borwein, Armin Straub, Special Values of Generalized Log-sine Integrals.
FORMULA
-Integral_{t=0..Pi} log(2*sin(t/2))^7 = (2835/4)*Pi*zeta(7) + (315/8)*Pi^3*zeta(5) + (133/32)*Pi^5*zeta(3).
Also equals 7th derivative of -Pi*binomial(x, x/2) at x=0.
EXAMPLE
5040.03987911504516434562143833539315930537596167748200200213853916...
MATHEMATICA
RealDigits[(2835/4)*Pi*Zeta[7] + (315/8)*Pi^3*Zeta[5] + (133/32)*Pi^5*Zeta[3], 10, 105] // First
PROG
(PARI) -intnum(t=0, Pi, log(2*sin(t/2))^7) \\ Hugo Pfoertner, Jul 22 2020
CROSSREFS
KEYWORD
AUTHOR
Jean-François Alcover, Jun 09 2015
STATUS
approved