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Sharp inequalities for the complete elliptic integral of the first kind. (English) Zbl 0906.33012

The author offers an improvement on one of two inequalities for the complete elliptic integral of the first kind by S. L. Qiu and M. K. Vamamurthy [SIAM J. Math. Anal. 27, 823-834 (1996; Zbl 0860.33014)] and the statement that the constants in the improved inequality and in the remaining one are the best possible.

MSC:

33E05 Elliptic functions and integrals

Citations:

Zbl 0860.33014
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