Laplace Transform of Periodic Function
Laplace Transform of Periodic Function:
A function f (t) is said to be periodic function with periods α > 0, if f (t a) = f (t)
Theorem: if f (t) is a periodic function of period α > 0, then
Substitute, t = u a in the second integral;
Similarly by substituting t = u 2α in the 3rd integrals, we get;
∴ equation (2) reduces to;
This completes the proof of the theorem.