There are some steps that if I apply them I can show that [imath]\displaystyle \mathscr{L}\{\text{erfc}{(\sqrt{t})}\} = \frac{1}{s}\left(1 - \frac{1}{\sqrt{s + 1}}\right)[/imath]. If I apply the same steps to find [imath]\displaystyle \mathscr{L}\bigg\{\text{erfc}\bigg(\frac{1}{\sqrt{t}}\bigg)\bigg\}[/imath], they don't work.
How do I show the following?
[imath]\displaystyle \mathscr{L}\bigg\{\text{erfc}\bigg(\frac{a}{2\sqrt{t}}\bigg)\bigg\} = \dfrac{e^{-a\sqrt{s}}}{s}[/imath]
Can the first identity help me to find the second identity or I have to start everything from scratch?
How do I show the following?
[imath]\displaystyle \mathscr{L}\bigg\{\text{erfc}\bigg(\frac{a}{2\sqrt{t}}\bigg)\bigg\} = \dfrac{e^{-a\sqrt{s}}}{s}[/imath]
Can the first identity help me to find the second identity or I have to start everything from scratch?