A bound for the error term in the Brent-McMillan algorithm
arXiv:1312.0039 · doi:10.1090/S0025-5718-2015-02931-7
Abstract
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.
10 pages, 1 table