As it can be read here, http://en.wikipedia.org/wiki/Laplace_transform#Relation_to_power_series the Laplace transform is a continuous analog of a power series in which the discrete parameter n is replaced by the continuous parameter t, and x is replaced by exp(-s). Therefore, computing a discrete power series or a continuous laplace transform should converge to the same function, is it right? Let's apply it for the simplest case: a(x)=1 For the discrete power series it converges to 1/1-x (provided that -1<x<1) For the continuous power series it converges to 1/s (provided that s>0) Now, this two should be equivalent right? If you substitute s=-ln(x) you get -1/ln(x), which is not the same as 1/1-x. What I am doing wrong?