Invert a Laplace Transform Using Post's Formula

Emil Post (1930) derived a formula for inverting Laplace transforms that relies on computing derivatives of symbolic order and sequence limits. Here, Post's inversion formula is implemented using the new capabilities of D and DiscreteLimit.

Post's inversion formula may be stated as follows.

Define a function that implements Post's inversion formula.

Compute the inverse Laplace transform of using the formula.

Obtain the same result using InverseLaplaceTransform.

Create a table of basic inverse Laplace transforms using Post's inversion formula.

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The Post formula can also be used for the numerical approximation of inverse Laplace transforms by using derivatives of sufficiently high order, as illustrated in the following.

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