Abstract
In the present investigation we first introduce normalized \(\tau \)-confluent hypergeometric function \(\varphi ^\tau (a;b;z)\) and then find sufficient conditions so that \(\varphi ^\tau (a;b;z)\) have certain geometric properties like close-to-convexity and starlikeness in the open unit disk \(\mathbb {D}\). Upper bound of \(|\varphi ^\tau (a;b;z)|\) and \(|\varphi ^\tau (a;b;z)'|\) are also determined.
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Bansal, D., Soni, A. & Soni, M.K. Geometric properties of \(\tau \)-confluent hypergeometric function. Anal.Math.Phys. 10, 73 (2020). https://doi.org/10.1007/s13324-020-00426-8
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DOI: https://doi.org/10.1007/s13324-020-00426-8
Keywords
- Analytic function
- Univalent function
- \(\tau \)-Confluent hypergeometric function
- Starlike function
- Close-to-convex function