Function No.

$f\left(s\right)$

$f\left(t\right)$

1

$\frac{1}{1+s^2}$

$\sin \left(t\right)$

2

$\frac{1}{{\left(s+1\right)}^2}$

$t{\text{e}}^{-t}$

3

$\frac{1}{s^2}$

t

4

$\frac{1}{\sqrt{s}}$

$\frac{1}{\sqrt{\pi t}}$

5

$\frac{\ln s}{s}$

$-\left(\ln t+\gamma \right)$

6

$\frac{1}{s}$

1

7

$\frac{1}{\sqrt{s^2+1}}$

$J\left(\mathrm{0,}t\right)$

8

$\frac{{\text{e}}^{s}K\left(\mathrm{1,}s\right)}{s}$

$\sqrt{t\left(t+2\right)}$

9

$\frac{1}{s+0.5}$

${\text{e}}^{-\frac{t}{2}}$

10

$\frac{1}{{\left(s+0.2\right)}^2+1}$

${\text{e}}^{-0.2t}\sin \left(t\right)$

11

$\arctan \left(\frac{1}{s}\right)$

$\frac{\sin \left(t\right)}{t}$