Generalized Elliptic Integrals and the Legendre M-function
Classical Analysis and ODEs
2015-06-26 v2 Complex Variables
Abstract
We study monotonicity and convexity properties of functions arising in the theory of elliptic integrals, and in particular in the case of a Schwarz-Christoffel conformal mapping from a half-plane to a trapezoid. We obtain sharp monotonicity and convexity results for combinations of these functions, as well as functional inequalities and a linearization property.
Cite
@article{arxiv.math/0701438,
title = {Generalized Elliptic Integrals and the Legendre M-function},
author = {V. Heikkala and H. Lindén and M. K. Vamanamurthy and M. Vuorinen},
journal= {arXiv preprint arXiv:math/0701438},
year = {2015}
}
Comments
28 pages