Generalized Elliptic Integrals and the Legendre M-function

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.

28 pages

References in corpus (2)

• Generalized Convexity and Inequalities
• On Rationally Parametrized Modular Equations

Cited by in corpus (6)

• Convexity and monotonicity for the elliptic integrals of the first kind and applications
• Topics in special functions III
• Reflections on Ramanujan's Mathematical Gems
• On generalized complete $(p,q)$-elliptic integrals
• Hypergeometric functions and hyperbolic metric
• Sharp bounds for generalized elliptic integrals of the first kind