Hypergeometric functions in geometric function theory. (English) Zbl 0948.30024

Vuorinen, Matti

Srinivasa Rao, K. (ed.) et al., Special functions and differential equations. Proceedings of a workshop, WSSF ’97, Madras, India, January 13-24, 1997. New Delhi: Allied Publishers Private Limited. 119-126 (1998).

A connection between special functions and a fundamental geometric property of quasiconformal maps of the unit disc, is discussed and a few of the numerous unpublished results left by S. Ramanujan in his notebooks at the time of his premature death are mentioned. Some open problems on generalized modular equations with signature \({1\over a}\) and order \(p\) defined by \[ {F(a,1-a;1;1-s^2)\over F(a,1-a;1;s^2)}= p{F(a,1-a;1;1-r^2)\over F(a,1-a;1;r^2)} \] are also given.
For the entire collection see [Zbl 0914.00063].

Reviewer: K.M.Saksena (Kanpur)

MSC:

30C62	Quasiconformal mappings in the complex plane
33C20	Generalized hypergeometric series, \({}_pF_q\)

Keywords:

asymptotic formula; quasiconformal maps