Do you know a litterature reference for the formula which generates the continues fraction for (1 + x)^0.5, please? There is a lot to be found in the web, regarding that fraction, but I have not been able to find out who came up with it... The formula that I have in mind is (1 + x)^0.5 = 1 + x / (1 + (1 + x)^0.5) (1) On the basis of that formula, I have used (1 + x)^0.5 # (3x + 4) / (x + 4) (2) after approximating (1 + x)^0.5 # 1 + x/2 (3) in the numerator in Eq.1. In other words, I contented myself with a single iteration of Eq.1. Eq. 2 gives (1 + x)^0.5 with a 1% error or less, for 0<x<1, by the way, whereas the error in Eq.3 is 6% for x=1. Thank you