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A series expansion of a function about an argument x0 is an expression of the form A + B(x - x0) + C(x - x0)2 + D(x - x0)3 + ... that can go on forever. These are amazingly useful. The condition that exp(x) is its own derivative gives relationships between the coefficients, A, B, C,... that allow you to deduce what they all are quickly, given A. |