[Adding subject; fixing bug.] Whoa, how are you getting these? Convergence is absent or useless. WDS> h(n) = (-1)^(parity of bit-sum of binary representation of n) f(x) S=SUM[ f(n) * h(n), for n=0..2^k-1 with k large] ln(x+1) S=-log(2)/2 ln(x+2) S = -0.1379330125 ln(x+3) -0.07070756527 x^j 0 for any fixed integer j>=0 1/(x+1) 0.398761088108 [http://isc.carma.newcastle.edu.au/advancedCalc identifies this as 3^(1/6)/Zeta[3]^(5/237)/3 . I'm surprised you didn't notice.] 1/(x+2) 0.1049709156499 sqrt(x) -0.63407426 1/sqrt(x+1) 0.1983140804979 -- Warren D. Smith With f(x):= 2^-(x+1), the quantities (1+S)/2 and (1-S)/2 are the only solutions t to Peano[t] = {t,1}. I.e., in the square-fill, they map straight to the top edge. --rwg