Web Reference: The error and complementary error functions occur, for example, in solutions of the heat equation when boundary conditions are given by the Heaviside step function. The error function and its approximations can be used to estimate results that hold with high probability or with low probability. The relationship between the error function Erf (x) and the cumulative probability of normeal distribution is presented. The error function is an entire function; it has no singularities (except that at infinity) and its Taylor expansion always converges. For, however, cancellation of leading terms makes the Taylor expansion unpractical.
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