As it can be read here, http://ift.tt/1we735j
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
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?
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?
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