Laplace Transform: Examples
that has positive radius of convergence R>0. Analytic functions are the best-behaved functions in all of calculus. For example, every analytic function is in nitely-di erentiable: Theorem: Let f(x) be analytic at x 0, say f(x) = X1 n=0 a n(x x 0)nwith radius of convergence R>0. Then: (a) fis in nitely-di erentiable on the interval (x 0 R;x 0 + R).
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