OFFSET
1,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..10000
Jonathan M. Borwein, Armin Straub, Special Values of Generalized Log-sine Integrals.
FORMULA
-Integral_{0..Pi} log(2*sin(t/2))^2 dx = -Pi^3/12.
Also equals 2nd derivative of -Pi*binomial(x, x/2) at x=0.
It can be noticed that Ls_2(Pi) is 0, and that Ls_2(Pi/2) is Catalan's constant 0.915966... (A006752).
EXAMPLE
-2.5838563900249850146230262555917829335187740471570923078453781753171...
MATHEMATICA
RealDigits[-Pi^3/12, 10, 103] // First
PROG
(PARI) -Pi^3/12 \\ G. C. Greubel, Aug 23 2018
(Magma) R:= RealField(100); -Pi(R)^3/12; // G. C. Greubel, Aug 23 2018
CROSSREFS
KEYWORD
AUTHOR
Jean-François Alcover, Jun 09 2015
STATUS
approved