Mathematics of Computation

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

 

 

Approximations for elliptic integrals


Author: Yudell L. Luke
Journal: Math. Comp. 22 (1968), 627-634
MSC: Primary 65.25
MathSciNet review: 0226825
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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 [Enhancements On Off] (What's this?)

  • [1] Yudell L. Luke, The Padé table and the 𝜏-method, J. Math. and Phys. 37 (1958), 110–127. MR 0099114
  • [2] 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.
  • [3] Paul F. Byrd and Morris D. Friedman, Handbook of elliptic integrals for engineers and physicists, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete. Bd LXVII, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1954. MR 0060642
  • [4] Yudell L. Luke, Simple formulas for the evaluation of some higher transcendental functions, J. Math. and Phys. 34 (1956), 298–307. MR 0078047

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DOI: http://dx.doi.org/10.1090/S0025-5718-1968-0226825-3
Article copyright: © Copyright 1968 American Mathematical Society