Contents of Complementary Error Function

f $\left(\vphantom{ t}\right.$ t $\left.\vphantom{ t}\right)$	F $\left(\vphantom{ s}\right.$ s $\left.\vphantom{ s}\right)$ = L $\left\{\vphantom{ f}\right.$ f $\left.\vphantom{ f}\right\}$ $\left(\vphantom{ s}\right.$ s $\left.\vphantom{ s}\right)$
$\limfunc$ erfc $\left(\vphantom{ \frac{a}{2\sqrt{t}}}\right.$ ${\frac{{a}}{{2\sqrt{t}}}}$ $\left.\vphantom{ \frac{a}{2\sqrt{t}}}\right)$ = 1 - $\func$ erf $\left(\vphantom{ \frac{a}{2\sqrt{t}}}\right.$ ${\frac{{a}}{{2\sqrt{t}}}}$ $\left.\vphantom{ \frac{a}{2\sqrt{t}}}\right)$	${\dfrac{{e^{-a\sqrt{s}}}}{{s}}}$
2 $\sqrt{{\frac{t}{\pi }}}$ e^-a²/4t - a $\limfunc$ erfc $\left(\vphantom{ \frac{a}{2\sqrt{t}% }}\right.$ ${\frac{{a}}{{2\sqrt{t}% }}}$ $\left.\vphantom{ \frac{a}{2\sqrt{t}% }}\right)$	${\dfrac{{e^{-a\sqrt{s}}}}{{s\sqrt{s}}}}$
e^abe^b²t $\limfunc$ erfc $\left(\vphantom{ b\sqrt{t}+\frac{a}{2\sqrt{t}}}\right.$ b $\sqrt{{t}}$ + ${\frac{{a}}{{2\sqrt{t}}}}$ $\left.\vphantom{ b\sqrt{t}+\frac{a}{2\sqrt{t}}}\right)$	${\dfrac{{e^{-a\sqrt{s}}}}{{\sqrt{s}\left( \sqrt{s}+b\right) }}}$
- e^abe^b²t $\limfunc$ erfc $\left(\vphantom{ b\sqrt{t}+\frac{a}{2\sqrt{t}}}\right.$ b $\sqrt{{t}}$ + ${\frac{{a}}{{2\sqrt{t}}}}$ $\left.\vphantom{ b\sqrt{t}+\frac{a}{2\sqrt{t}}}\right)$ + $\limfunc$ erfc $\left(\vphantom{ \frac{a}{2\sqrt{t}}}\right.$ ${\frac{{a}}{{2\sqrt{t}}}}$ $\left.\vphantom{ \frac{a}{2\sqrt{t}}}\right)$	${\frac{{be^{-a\sqrt{% s}}}}{{s\left( \sqrt{s}+b\right) }}}$