Hypergeometric functions and elliptic integrals. (English) Zbl 0984.33502

Anderson, G. D.; Vamanamurthy, M. K.; Vuorinen, M.

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].

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