OFFSET
3,1
LINKS
Jonathan M. Borwein, Armin Straub, Special Values of Generalized Log-sine Integrals.
FORMULA
-Integral_{0..Pi/3} log(2*sin(x/2))^5 dx = -74369*Pi^7/326592 - (15/2) * Pi * Zeta[3]^2 + 135*Gl_{6, 1}(Pi/3), where Gl is the multiple Glaisher function.
Also equals -720 * 7F6(1/2,1/2,...; 3/2,3/2,...; 1/4) (with 7F6 the hypergeometric function).
EXAMPLE
-720.1245682263318010530293318351565689006935502658088138930137116778...
MATHEMATICA
RealDigits[-720*HypergeometricPFQ[Table[1/2, {7}], Table[3/2, {6}], 1/4], 10, 103] // First
CROSSREFS
KEYWORD
AUTHOR
Jean-François Alcover, Jun 09 2015
STATUS
approved