Anderson, G. D.; Vamanamurthy, M. K.; Vuorinen, M. Hypergeometric functions and elliptic integrals. (English) Zbl 0984.33502 Srivastava, H. M. (ed.) et al., Current topics in analytic function theory. Singapore: World Scientific. 48-85 (1992). Summary: This work is mainly a survey of some recent results obtained by the present authors on hypergeometric functions, complete elliptic integrals, and related functions. The emphasis is on functions that arise in the study of conformal and quasiconformal mappings. Some new results, conjectures, and open problems are also included.For the entire collection see [Zbl 0976.00007]. Cited in 20 Documents MSC: 33E05 Elliptic functions and integrals 33C05 Classical hypergeometric functions, \({}_2F_1\) 30C62 Quasiconformal mappings in the complex plane 33-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to special functions 33C75 Elliptic integrals as hypergeometric functions Keywords:elliptic integrals PDF BibTeX XML Cite \textit{G. D. Anderson} et al., in: Current topics in analytic function theory. Singapore: World Scientific. 48--85 (1992; Zbl 0984.33502) Digital Library of Mathematical Functions: §19.9(i) Complete Integrals ‣ §19.9 Inequalities ‣ Legendre’s Integrals ‣ Chapter 19 Elliptic Integrals