Convergence of a power series

The coefficients are found from the orthonormal behavior of sine and cosine functions, which we will discuss later in the chapter. Fourier series differ from power series expansions in at least two important ways. First, the interval of convergence of a power series is different for different functions the Fourier series, on the other hand, always converges between —n and -l- r. Second, many functions cannot be expanded in a power series, whereas it is rare to find a function that cannot be expanded in a Fourier series. 

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