Generalized elliptic integrals
Classical Analysis and ODEs
2007-08-08 v2 Complex Variables
Abstract
Jacobi's elliptic integrals and elliptic functions arise naturally from the Schwarz-Christoffel conformal transformation of the upper half plane onto a rectangle. In this paper we study generalized elliptic integrals which arise from the analogous mapping of the upper half plane onto a quadrilateral and obtain sharp monotonicity and convexity properties for certain combinations of these integrals, thus generalizing analogous well-known results for classical conformal capacity and quasiconformal distortion functions.
Cite
@article{arxiv.math/0701436,
title = {Generalized elliptic integrals},
author = {Ville Heikkala and Mavina K. Vamanamurthy and Matti Vuorinen},
journal= {arXiv preprint arXiv:math/0701436},
year = {2007}
}
Comments
32 pages, 4 figures