Definition
In this section, ƒ(x) denotes a function of the real variable x. This function is usually taken to be periodic, of period 2π, which is to say that ƒ(x + 2π) = ƒ(x), for all real numbers x. We will attempt to write such a function as an infinite sum, or series of simpler 2π–periodic functions. We will start by using an infinite sum of sine and cosine functions on the interval, as Fourier did (see the quote above), and we will then discuss different formulations and generalizations.
Read more about this topic: Fourier Series
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—Ralph Waldo Emerson (1803–1882)
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