1 Aug
2010
1 Aug
'10
7:42 p.m.
Sum[(-Log[2])*Log[x] + 2^n*(Pi^2/12 + PolyLog[2, -x^(-2^(-n))]), {n, 0, Infinity}] -> -(Pi^2/12) + Log[x] - Log[x]*Log[2*Log[x]] + (1/2)*PolyLog[2, 1/x^2] Doesn't look too convergent, does it? Mma doubts it too. But In[389]:= MapAt[22 &, %, {1, 2, 3}] /. x -> .69 Out[389]= -0.0716747 -> -0.0716748 - 2.22045*10^-16 I I think there are 3^-n versions of this as well. --rwg