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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


A bound for the error term in the Brent-McMillan algorithm
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by Richard P. Brent and Fredrik Johansson PDF
Math. Comp. 84 (2015), 2351-2359 Request permission


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 the Bessel functions $I_0(x)$ and $K_0(x)$ for positive real $x$.
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Additional Information
  • Richard P. Brent
  • Affiliation: Mathematical Sciences Institute, Australian National University, Canberra, ACT 0200, Australia
  • Email:
  • Fredrik Johansson
  • Affiliation: RISC, Johannes Kepler University, 4040 Linz, Austria
  • MR Author ID: 999321
  • Email:
  • Received by editor(s): November 29, 2013
  • Received by editor(s) in revised form: January 1, 2014
  • Published electronically: March 4, 2015
  • Additional Notes: The first author was supported by Australian Research Council grant DP140101417.
    The second author was supported by the Austrian Science Fund (FWF) grant Y464-N18.
  • © Copyright 2015 American Mathematical Society
  • Journal: Math. Comp. 84 (2015), 2351-2359
  • MSC (2010): Primary 33C10, 11Y60, 65G99, 65Y20, 68Q25, 68W40, 68W99
  • DOI:
  • MathSciNet review: 3356029