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Convolutions with Hypergeometric Functions

Durai, M. Anbu, and Parvatham, R., (2000) Convolutions with Hypergeometric Functions. Bulletin of the Malaysian Mathematical Sciences Society, 23 (2). pp. 153-161. ISSN 0126-6705

Full text not available from this repository.

Official URL: http://math.usm.my/bulletin/pdf/v23n2/v23n2p6.pdf

Affiliations

University of Madras, Ramanujan Institute for Advanced Study in Mathematics

Abstract

In this paper we study the behaviour of $ [I_{a,b,c} (f)] (z) = zF (a,b,c,z)\ast f(z) $ where $ F(a,b,c, z) $ is the Gaussian Hypergeometric function and the $\ast$ is usual Hadamard product. In the main result, we find conditions on $ a,b,c,A,B $ and $\beta$ so that $ [I_{a,b,c} (f)](z) $ belong to $S^\ast [A,B]$ whenever $ f(z) \in R(\beta), \beta < 1$.

Item Type:Journal
Keywords:hypergeometric functions, starlikeness, subordination, Hadamard product.
Subjects:Q Science, Computer Science
ID Code:1317

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