Computing Bernoulli and Tangent numbers

Abstract

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

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

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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