Generalized Elliptic Integrals and the Legendre M-function
V. Heikkala, H. Lindén, M. K. Vamanamurthy, M. Vuorinen
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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