## Monday Math 106

The Laplace Transform
Part 7: Periodic functions

Let us consider a general periodic function f(x), with period T, and its Laplace transform. From the definition of the Laplace transform,
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Now, dividing up the region of integration into (infinitely many) intervals of length T, we get
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Next, on each integral term, we perform the substitution u=tnT, which gives us
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