Fourier Series Notation

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Can fourier series notation be written in different ways but get the same result? I ask because I've seen these two diferent notations. What is the difference between the two? If they produce the same result I will just keep using the first one, as I am more comfertable with it. Thanks :)

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and this notation:

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$$ k\omega t = \frac{2\pi kt} T \quad\text{if} \quad \omega = \frac{2\pi} T \quad \text{or} \quad T=\frac{2\pi} \omega. $$