Jump discontinuity refers to a specific type of discontinuity in a function where there is a sudden 'jump' in the function's value at a particular point. This occurs when the left-hand limit and the right-hand limit at that point do not equal each other, resulting in a distinct gap or jump between the two values. Understanding jump discontinuities is crucial when examining piecewise functions and their convergence properties, particularly in the context of Fourier series and the Gibbs phenomenon.
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