This video says that the formula for a Fourier Series is
$$f(x)≈a_0+\sum_{n=1}^N\left[a_n\cos\left(\frac{n\pi}{L}x\right)+b_n\sin\left(\frac{n\pi}{L}x\right)\right]$$
But Wikipedia says that the formula is
$$s_N(x)≈\frac{a_0}{2}+\sum_{n=1}^N \left[a_n\cos\left(\frac{2\pi}{P}nx\right)+b_n\sin\left(\frac{2\pi}{P}nx\right)\right]$$
My question is: Are these two equations equivalent? If so, how can we write $L$ in terms of $P$ and $n$? Any help would be greatly appreciated.
NOTE: Please don't close this question for vagueness; not all math problems involve a mathematical calculation.
Community wiki answer so the question can be marked as answered:
As noted in the comments, the use of different symbols $L$ and $P$ for the period and the relative factor of $2$ between the two definitions of $a_0$ doesn’t make the representations inequivalent.