Skip to content

InverseLaplaceTransform

Symbolic inverse Laplace transform.

$ wo 'InverseLaplaceTransform[1/(s^2 + 1), s, t]'
Sin[t]

A square root of s^2 + a^2 in the denominator inverts to a Bessel function.

$ wo 'InverseLaplaceTransform[1/Sqrt[s^2 + a^2], s, t]'
BesselJ[0, a*t]

The third argument names the point the inverse transform is taken at, so it may be an expression or a number rather than a plain symbol.

$ wo 'InverseLaplaceTransform[1/(s + 1), s, 2 u]'
E^(-2*u)

$ wo 'InverseLaplaceTransform[1/Sqrt[s^2 + 1], s, 1.5]'
0\.511827671735918\d (regex)