Inverse Laplace transform of $ \bar{U}(r,s) = \frac{1}{s} \frac{K_0 \left(\sqrt{s/\alpha} \, r \right)}{K_0 \left(\sqrt{s/\alpha} \, b \right)}$

Question

What is the inverse Laplace transform of $$ \bar{U}(r,s) = \frac{1}{s} \frac{K_0 \left(\sqrt{s/\alpha} \, r \right)}{K_0 \left(\sqrt{s/\alpha} \, b \right)} \tag{12}. $$ ?

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