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arXiv · 1507.01383

Complete $(p,q)$-elliptic integrals with application to a family of means

Toshiki Kamiya·Shingo Takeuchi
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Abstract

The complete elliptic integrals are generalized by using the generalized trigonometric functions with two parameters. It is shown that a particular relation holds for the generalized integrals. Moreover, as an application of the integrals, an alternative proof of a result for a family of means by Bhatia and Li, which involves the logarithmic mean and the arithmetic-geometric mean, is given.

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Toshiki Kamiya, Shingo Takeuchi. 2015-11-24. Complete $(p,q)$-elliptic integrals with application to a family of means. https://doi.org/10.7153/jca-10-02

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