notes 10-3 - SECTION 10.3 WHEN DOES A FOURIER SERIES...

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SECTION 10.3 WHEN DOES A FOURIER SERIES CONVERGE? THE FOURIER CONVERGENCE THEOREM. Suppose that f is originally defined for - L x < L and the definition is then extended so that f is periodic with period 2 L . Suppose also that then f and f 0 are piecewise continuous on the interval - L x L . Then the Fourier series whose coefficients are given by the Euler-Fourier formulas converges to f ( x ) at points where f is continuous and to f ( x +) + f ( x - ) 2 at points where f is discontinuous. Piecewise continuous means that f is continuous everywhere except for finitely many points
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