The Euler - Maclaurin Expansion
نویسنده
چکیده
We have seen that the accuracy of methods for computing integrals or derivatives of a function f(x) depends on the spacing between points at which f is evaluated, and that the approximation tends to the exact value as this spacing tends to 0. Suppose that a uniform spacing h is used. We denote by F (h) the approximation computed using the spacing h, from which it follows that the exact value is given by F (0). Let p be the order of accuracy in our approximation; that is,
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