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Some bounds for the complete elliptic integrals of the first and second kinds. (English) Zbl 1217.26042

Summary: The complete elliptic integrals of the first and second kinds are bounded by using the power series expansions of some functions, the celebrated Wallis inequality, and an integral inequality due to R. P. Agarwal, P. Cerone, S. S. Dragomir and F. Qi.

MSC:

26D15 Inequalities for sums, series and integrals
33C75 Elliptic integrals as hypergeometric functions
33E05 Elliptic functions and integrals
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