Geometric properties of basic hypergeometric functions

In this article, we consider basic hypergeometric functions introduced by Heine. We study the mapping properties of certain ratios of basic hypergeometric functions having shifted parameters and show that they map the domains of analyticity onto domains convex in the direction of the imaginary axis....

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Bibliographic Details
Published in:Journal of difference equations and applications Vol. 20; no. 11; pp. 1502 - 1522
Main Authors: Agrawal, S., Sahoo, S.K.
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 02.11.2014
Taylor & Francis Ltd
Subjects:
continued fraction
convexity in the direction of the imaginary axis
Difference equations
g-fraction
Gauss and basic hypergeometric functions
Geometry
Hausdorff moment sequence
Hypergeometric functions
Mapping
Mathematical analysis
Mathematical functions
q-difference operator
univalent, starlike and close-to-convex functions
ISSN:1023-6198, 1563-5120
Online Access:Get full text
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Summary:In this article, we consider basic hypergeometric functions introduced by Heine. We study the mapping properties of certain ratios of basic hypergeometric functions having shifted parameters and show that they map the domains of analyticity onto domains convex in the direction of the imaginary axis. In order to investigate these mapping properties, some useful identities are obtained in terms of basic hypergeometric functions. In addition, we find conditions under which the basic hypergeometric functions are in a q-close-to-convex family.
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ISSN:1023-6198
1563-5120
DOI:10.1080/10236198.2014.946501