If $$\mathcal{L}\{f(t)\} = F(s)$$ then I know that $$\mathcal{L}\{f(t - a)H(t - a)\} = e^{-as}F(s) = e^{-as}\mathcal{L}\{f(t)\}$$ Also using the above I can find that $$\mathcal{L}\{f(t)H(t - a)\} = e^{-as}\mathcal{L}\{f(t + a)\}$$ How do I represent $\mathcal{L}\{f(t + a)\}$ in some shifted form of $F(s)$?
Note that $H(t)$ is the Heaviside unit step function.
I need this information because it will be helpful while solving differential equations using Laplace Transforms which involve Heaviside step functions.