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Asymptotic expansions and inequalities for hypergeometric function

Published online by Cambridge University Press:  26 February 2010

S. Ponnusamy  and
M. Vuorinen
S. Ponnusamy
Affiliation:
Department of Mathematics, Indian Institute of Technology, Institution of Engineers Building, Panbazar, Guwahati-781 001, India. e-maii: [email protected]
M. Vuorinen
Affiliation:
Department of Mathematics, P.O. Box 4, (Yliopistonkatu 5), FIN-000 14, University of Helsinki, Finland. e-mail: [email protected]
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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.

MSC classification

Secondary: 33C05: Classical hypergeometric functions, $_2F_1$
Type
Research Article
Information
Mathematika , Volume 44 , Issue 2 , December 1997 , pp. 278 - 301
Copyright
Copyright © University College London 1997

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