Mathematika

Research Article

Asymptotic expansions and inequalities for hypergeometric function

S. Ponnusamya1 and M. Vuorinena2

a1 Department of Mathematics, Indian Institute of Technology, Institution of Engineers Building, Panbazar, Guwahati-781 001, India. e-maii: samy@iitg.ernet.in

a2 Department of Mathematics, P.O. Box 4, (Yliopistonkatu 5), FIN-000 14, University of Helsinki, Finland. e-mail: vuorinen@csc.fi

Abstract

Ramanujan's work on the asymptotic behaviour of the hypergeometric function has been recently refined to the zero-balanced Gaussian hypergeometric function F(a, b; a + b; x) as x→1.We extend these results for F(a, b; c; x) when a, b, c>0 and c<a + b.

(Received March 23 1995)

Key Words:

  • 33C05: SPECIAL FUNCTIONS: Hypergeometric junctions: Classical hypergeometric functions.