Inverse Laplace Transform Table Error Function
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Integral Of Error Function
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Laplace Transform Of Complementary Error Function
answer The best answers are voted up and rise to the top An inverse Laplace transform involving Error function up vote 1 down vote favorite 1 Dear MOs, I need to calculate the inverse Laplace transform of the following function $$ g_a(z) = \frac{e^{a z}\: \text{erfc}(\sqrt{a z})}{\sqrt{z}-2},\quad a>0. $$ I have checked, among many others, the book "Table of Integral Transform, erfc laplace transform Vol. I". In P.267, Eq. (14) is for $$ g(z) = \frac{e^{a z}\: \text{erfc}(\sqrt{a z})}{\sqrt{z}} $$ which is almost what I need. Other than this formula, I didn't find the one that I need. I have tried mathematica, which couldn't give an answer. I think the hope to find out the solution is quite small. EIDT: here is some motivation of the problem. Suppose the inverse transform gives us a function $f_a(t)$. I want to see the limit $$\lim_{a\rightarrow 0_+} f_a(t)=?$$ Can I simply do this: $$ \lim_{a \rightarrow 0_+} \mathcal{L}^{-1}\left(g_a\right)(t) \stackrel{?}{=} \mathcal{L}^{-1}\left(\lim_{a\rightarrow 0_+} g_a\right)(t) = \mathcal{L}^{-1}\left(g_0\right)(t) =\frac{1}{\sqrt{\pi t}} + 2 e^{4t} \text{erfc}(-2\sqrt{t}) $$ Are there some Lebesgue's dominated convergence theorems to use in complex analysis? Thank you very much for any hints! Anand laplace-transform integral-transforms special-functions ca.analysis-and-odes share|cite|improve this question edited Jun 2 '12 at 21:10 asked Jun 2 '12 at 17:42 Anand 75411122 2 Perhaps you may expand $(\sqrt{z}-2)^{-1}$ in powers of $z$ then multiply by $e^{az} \text{erfc}(az)$ and apply Laplace transform to each term. The resulting terms would be derivatives one of the others. Possibly obtain a
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