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jasonRF

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I am assuming you are using the single-sided Laplace transform, with the standard definition

$$F(s) = \int_0^\infty f(t) e^{-s t} dt$$

so the region of convergence a right half-plane ##\Re(s)>s_0## (where the notation ##\Re(s)## indicates the real part of ##s##). This means that ##F(s)## is analytic in that half-plane, and in general is not defined outside of that half-plane. However, in many cases ##F(s)## can be extended so that it is analytic in a larger region of the complex plane (this is called

If the term

Note that in some cases the process of analytic continuation is much more complicatd. However, in the types of problems you are likely to find in basic electronics, ##F(s)## is often a rational function, so is trivially its own analytic continuation into the entire complex plane except at the poles of ##F(s)##.

Jason

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