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Asymptotic approximations for symmetric elliptic integrals. (English) Zbl 0794.41021

Symmetric elliptic integrals are homogeneous functions of three or four variables. When some of the variables are much larger than the others, asymptotic approximations to them are given with error bounds. Further, the symmetric elliptic integrals of the first, second, and third kinds are proved to be linearly independent with respect to coefficients that are rational functions.

MSC:

41A50 Best approximation, Chebyshev systems
33E05 Elliptic functions and integrals
26D15 Inequalities for sums, series and integrals
26D20 Other analytical inequalities
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