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A method for finding the asymptotic behavior of a function from its Laplace transform Froese Fischer, Charlotte

Abstract

In many practical problems, particularly in circuit analysis, the Laplace Transform method is used to solve linear differential equations. When only the asymptotic behaviour at infinity of the solution is of interest, it is not necessary to find the exact solution. We have developed a method for finding the asymptotic behaviour of a function directly from its Laplace transform. The method is a generalization of one given by Doetsch [5,6]. The behaviour of a function F(t) for large t depends upon the singularities of its transform f(s) on the line to the right of which f(s) is regular. The asymptotic behaviour of F(t) is expressed in terms of comparison functions G(k)(t) whose transforms have the same singularities as f(s). We have considered singularities such as L/s(v+l), (ℓns) n/s (v+1), l/s(v+1)ℓns, e(-k/s) / s(v+1), (ℓns)ne(-k/s) / s(v+1), or e(-k/s) / s(v+1) ℓns. The first two have been studied extensively by Doetsch.

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