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Mathematics of Computation

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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.


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