Question

Let f satisfy f(t + T) = f(t) for all t>=0 and for some fixed positive number T; f is said to be periodic with period T on 0 <= t <= infinity. Show that:
\[L [f(t)] = \frac{ \int\limits_{0}^{T} e ^{-st}f(t)dt }{ 1-e ^{-sT} }\]

L is the Laplace operator