## 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

**Proof: **

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.