# Computing Bernoulli and Tangent numbers

Brent, Richard

### Abstract

*TeX Embedding failed!* are rational numbers *TeX Embedding failed!* defined by the generating function

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They are of interest in number theory and are related to special values of the Riemann zeta function. They also occur as coefficients in the Euler-Maclaurin formula. The closely related *TeX Embedding failed!* *TeX Embedding failed!*, defined by

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are more convenient for computation because they are integers. In this talk I will consider some algorithms for computing Bernoulli and Tangent numbers. In particular, I will give a very simple in-place algorithm for computing the first *TeX Embedding failed!* Tangent numbers using *TeX Embedding failed!* integer operations. Although this is not the asymptotically fastest algorithm, it is extremely simple and convenient for moderate values of *TeX Embedding failed!*.

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