Generalized elliptic integrals and the Legendre M-function

: Heikkala V., Lindén H., Vamanamurthy M., Vuorinen M.

: 2008

: Journal of Mathematical Analysis and Applications

: 338

: 1

: 223

: 243

: 21

: 0022-247X

DOI: https://doi.org/10.1016/j.jmaa.2007.05.020

: http://api.elsevier.com/content/abstract/scopus_id:34548859833

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. © 2007 Elsevier Inc. All rights reserved.