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{{#category_index:E|eigenfunction}} (ī g∂n fun, sh∂n) One of a set of functions that satisfies both a differential equation and a set of boundary conditions. For example, a stretched string or an organ pipe might vibrate in a number of modes, each with a characteristic frequency (eigenfrequency, eigenvalue, or characteristic root). The superposition of these eigenfunctions is the general solution. The eigenfunctions corresponding to different eigenvalues are orthogonal (or independent). ‘‘Eigen’’ is German for ‘‘characteristic.’’