English

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.

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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