I'm after the numerical inverse Laplace transform of a function, so I type
f[t_?NumericQ] := InverseLaplaceTransform[1/(1 + s + ArcTanh[1/(s - 1)]), s, t];
This function may possibly suck, but it looks like its inverse Laplace transform should exist, albeit not in closed form (for instance, by the initial value theorem we know that f[t->0+]=1
). However, when confronted with this task Mathematica simply replicates my command without giving a numerical solution.
Of course ArcTanh
is a multivalued function in the complex plane, but shouldn't the algorithm used for Laplace inversion know how to handle this?
InverseLaplaceTransform
was introduced in version12.2
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