Anderson, G. D.; Vamanamurthy, M. K.; Vuorinen, M. Functional inequalities for complete elliptic integrals and their ratios. (English) Zbl 0692.33001 SIAM J. Math. Anal. 21, No. 2, 536-549 (1990). The main purpose of this article is to improve some functional inequalities satisfied by complete elliptic integrals of the first kind. These inequalities are sharp and generalize the functional identity of Landen. Some applications important in quasiconformal analysis are discussed. Reviewer: N.Kostov Cited in 1 ReviewCited in 64 Documents MSC: 33E05 Elliptic functions and integrals 33E99 Other special functions 30C62 Quasiconformal mappings in the complex plane Keywords:Teichmüller ring; Grötzsch ring; functional inequalities; complete elliptic integrals PDFBibTeX XMLCite \textit{G. D. Anderson} et al., SIAM J. Math. Anal. 21, No. 2, 536--549 (1990; Zbl 0692.33001) Full Text: DOI