Complete $(p,q)$-elliptic integrals with application to a family of means
arXiv:1507.01383 · doi:10.7153/jca-10-02
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.
13 pages