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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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Approximations for elliptic integrals
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by Yudell L. Luke PDF
Math. Comp. 22 (1968), 627-634 Request permission

Abstract:

Closed-form approximations are derived for the three kinds of incomplete elliptic integrals by using the Padé approximations for the square root. An effective analytical representation of the error is presented. Approximations for the complete integrals based on trapezoidal-type integration formulae are also developed.
References
  • Yudell L. Luke, The PadĂ© table and the $\tau$-method, J. Math. and Phys. 37 (1958), 110–127. MR 99114, DOI 10.1002/sapm1958371110
  • I. M. Longman, “The application of rational approximations to the solution of problems in theoretical seismology,” Bull. Seismological Soc. America, v. 56, 1966, pp. 1045–1065.
  • Paul F. Byrd and Morris D. Friedman, Handbook of elliptic integrals for engineers and physicists, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer BerĂĽcksichtigung der Anwendungsgebiete. Band LXVII, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1954. MR 0060642
  • Yudell L. Luke, Simple formulas for the evaluation of some higher transcendental functions, J. Math. and Phys. 34 (1956), 298–307. MR 78047, DOI 10.1002/sapm1955341298
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Additional Information
  • © Copyright 1968 American Mathematical Society
  • Journal: Math. Comp. 22 (1968), 627-634
  • MSC: Primary 65.25
  • DOI: https://doi.org/10.1090/S0025-5718-1968-0226825-3
  • MathSciNet review: 0226825