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A bound for the error term in the Brent-McMillan algorithm

The Brent-McMillan algorithm B3 (1980), when implemented with binary splitting, is the fastest known algorithm for high-precision computation of Euler's constant. However, no rigorous error bound for the algorithm has ever been published. We provide such a bound and justify the empirical observations of Brent and McMillan. We also give bounds on the error in the asymptotic expansions of functions related to modified Bessel functions.

preprint2013arXivOpen access
Richard P. BrentFredrik Johansson
math.NA
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Richard P. BrentFredrik Johansson

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