【原】开特仑(Catalan)常数ε(2)

ε(2)=∑(n=1…∞)(-1)^n-1/(2n-1)²

      =0.919565594177219015054603514932……

      =∫(0,1)(1/x)arctan(x)dx

      =2∫(0,π/4)lncos(x)dx+(π/2)ln2

      =(-2)∫(0,π/4)lnsin(x)dx-(π/2)ln2

      =(1/2)∫(0,π/2)[x/sin(x)]dx

      =(π/2)∫(0,1)[1/(1+x²)²][(x²-1)/ln(x)]dx

卡特兰常数ε(2)