Generalized Elliptic Integrals and the Legendre M-function

Details Generalized Elliptic Integrals and the Legendre M-function Generalized Elliptic Integrals and the Legendre M-function

2007-01-16

arxiv.org/abs/math/0701438v2

Mathematics

Classical Analysis and ODEs

28 pages

Scientific paper

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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