Half range Fourier series

Half range Fourier series is a way of using math to represent a pattern that goes up and down over and over again. Instead of using just one kind of math, we use two kinds! The first kind of math is called a Fourier series. This series has a pattern that goes up and down (like a wave). We use the Fourier series to represent the first half of the pattern (from 0 to the middle). Then, we use a different kind of math to represent the second half of the pattern (from the middle to the top). The two math patterns together make one pattern that shows us the full pattern!