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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.

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Precise and fast computation of the general complete elliptic integral of the second kind
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by Toshio Fukushima PDF
Math. Comp. 80 (2011), 1725-1743 Request permission

Abstract:

We developed an efficient procedure to evaluate two auxiliary complete elliptic integrals of the second kind $B(m)$ and $D(m)$ by using their Taylor series expansions, the definition of Jacobi’s nome, and Legendre’s relation. The developed procedure is more precise than the existing ones in the sense that the maximum relative errors are 1-3 machine epsilons, and it runs drastically faster; around 5 times faster than Bulirsch’s cel2 and 16 times faster than Carlson’s $R_F$ and $R_D$.
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Additional Information
  • Toshio Fukushima
  • Affiliation: National Astronomical Observatory of Japan, 2-21-1, Ohsawa, Mitaka, Tokyo 181-8588, Japan
  • Email: Toshio.Fukushima@nao.ac.jp
  • Received by editor(s): February 10, 2010
  • Received by editor(s) in revised form: April 22, 2010
  • Published electronically: February 1, 2011
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 80 (2011), 1725-1743
  • MSC (2010): Primary 33E05
  • DOI: https://doi.org/10.1090/S0025-5718-2011-02455-5
  • MathSciNet review: 2785476