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Approximations for Elliptic Integrals

Yudell L. Luke
Mathematics of Computation
Vol. 22, No. 103 (Jul., 1968), pp. 627-634
DOI: 10.2307/2004539
Stable URL: http://www.jstor.org/stable/2004539
Page Count: 8
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Approximations for Elliptic Integrals
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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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