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Approximations for elliptic integrals


Author: Yudell L. Luke
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
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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] Y. L. Luke, ``The Padé table and the $ \tau $-method,'' J. Math. Phys., v. 37, 1958, pp. 110-127. MR 20 #5558. MR 0099114 (20:5558)
  • [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] P. F. Byrd & M. D. Friedman, Handbook of Elliptic Integrals for Engineers and Physicists, Springer-Verlag, New York, 1954. MR 15, 702. MR 0060642 (15:702a)
  • [4] Y. L. Luke, ``Simple formulas for the evaluation of some higher transcendental functions,'' J. Math. Phys., v. 34, 1956, pp. 298-307. MR 17, 1138. MR 0078047 (17:1138e)

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Additional Information

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

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