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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.

In[1]:=1

Compute the inverse Laplace transform of using the formula.

In[2]:=2
Out[2]=2

Obtain the same result using InverseLaplaceTransform.

In[3]:=3
Out[3]=3

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

show complete Wolfram Language input
In[4]:=4
Out[4]//TraditionalForm=4]//TraditionalForm=

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.

In[5]:=5
In[6]:=6
In[7]:=7
Out[7]=7

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