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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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.


Iterated square root expansions for the inverse cosine and inverse hyperbolic cosine
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by Henry C. Thacher PDF
Math. Comp. 15 (1961), 399-403 Request permission


Let ${R_1} = \sqrt {2 + 2x}$, ${R_{k + 1}} = \sqrt {|{2 + {R_k}}|}$. Then ${2^k}\sqrt {|{2 - {R_k}}|}$ and ${2^k}{\{ |{6 - 2\sqrt {3 + 3{R_k}} }|\} ^{1/2}}$ both converge to $\arccos x$ if $|x| \leqq 1$ and to $\operatorname {arccosh} x$ if $1 \leqq x < \infty$. Truncation errors for the two expressions are of the order of 2$^{-2k}$ and 2$^{-4k}$, respectively.
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Additional Information
  • © Copyright 1961 American Mathematical Society
  • Journal: Math. Comp. 15 (1961), 399-403
  • MSC: Primary 65.20
  • DOI:
  • MathSciNet review: 0135228