Electronics/Laplace Transform pairs

Current revision (unreviewed)

$f (t)$	$F (s)$
$δ(t - t 0)$	$e^{-st_0}$
$u (t)$	$\frac{1}{s}$
$e - α t u (t)$	$\frac{1}{s+\alpha}$
$sin(β t) u (t)$	$\frac{\beta}{s^2+\beta^2}$
$cos(β t) u (t)$	$\frac{s}{s^2+\beta^2}$
$e - α t sin(β t) u (t)$	$\frac{\beta}{(s+\alpha)^2+\beta^2}$
$e - α t cos(β t) u (t)$	$\frac{s+\alpha}{(s+\alpha)^2+\beta^2}$
$2 e α t (a cosβ t - b sinβ t) u (t)$	$\frac{a+jb}{s+\alpha-j\beta}+\frac{a-jb}{s+\alpha+j\beta}$
$t n$	$\frac{n!}{s^{n+1}}$
$t n f (t)$	$(-1)^n\frac{d^nF(s)}{ds^n}$
$\frac{df(t)}{dt}$	$s F (s) - f (0)$
$\int_0^tf(x) dx$	$\frac{1}{s}F(s)$
$u - 1 (t - t 0) f (t - t 0)$	$e^{-t_0s}F(s), t_0 \ge 0$
$h(t)*f(t)=\int_0^th(t-\tau)f(\tau) d\tau$	$H (s) F (s)$
$f 1 (t) f 2 (t)$	$F 1 (s) * F 2 (s)$