Complete $(p,q)$-elliptic integrals with application to a family of means
Classical Analysis and ODEs
2019-03-12 v2 Analysis of PDEs
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.
Keywords
Cite
@article{arxiv.1507.01383,
title = {Complete $(p,q)$-elliptic integrals with application to a family of means},
author = {Toshiki Kamiya and Shingo Takeuchi},
journal= {arXiv preprint arXiv:1507.01383},
year = {2019}
}
Comments
13 pages