# Inverse Laplace Transform of the Following Solution

I have solved thermal energy balance equation during cold fluid injection into a semi-infinite model. I obtained the following solution in Laplace domain.

$$\bar T_D = \frac{r_D^vK_v(\sqrt[]s r_D)}{sK_v(\sqrt[]s)}$$

How can I obtain inverse Laplace transformation of this solution given $$K_v$$ is modified Bessel function of second kind and order $$v$$. $$v$$ is an integer number higher than zero.

• What is the specific function $K$? Oct 3, 2019 at 18:41
• Kv is Modified Bessel function of second kind and integer order v. @Mattos Oct 3, 2019 at 18:42
• Most likely you'll have to do the complex line integral definition of the ILT. Oct 3, 2019 at 18:54
• I hope anyone can help me obtain this inversion. I am sorry but as a petroleum engineer, my mathematical skills are not high.@AdrianKeister Keister Oct 3, 2019 at 19:02
• It seems someone has already tried something very similar here. Oct 4, 2019 at 15:07