OFFSET
1,1
LINKS
J. M. Borwein, I. J. Zucker and J. Boersma, The evaluation of character Euler double sums, The Ramanujan Journal, April 2008, Volume 15, Issue 3, pp 377-405, see p. 15 l_2.
FORMULA
L_2 = -Pi^3/24 - (1/2)*Sum_{m >= 1} (Sum_{n=1..m} ((-1)^(n-1)/(2*n-1))/m^2).
EXAMPLE
-2.0335765060720546009120689697005182499923760756130461855 ...
MAPLE
evalf(-Pi^3/24 - (1/2)*sum(sum((-1)^(n-1)/(2*n-1)/m^2, n=1..m), m=1..infinity), 100) # Vaclav Kotesovec, Sep 18 2014
MATHEMATICA
digits = 100; L2 = -NIntegrate[Log[2*Sin[t/2]]^2, {t, 0, Pi/2}, WorkingPrecision -> digits+10]; RealDigits[L2, 10, digits] // First
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jean-François Alcover, Sep 18 2014
STATUS
approved