Geometric Properties of the Shifted Hypergeometric Functions

Toshiyuki Sugawa; Li Mei Wang

doi:10.1007/s11785-017-0674-4

Geometric Properties of the Shifted Hypergeometric Functions

Toshiyuki Sugawa, Li Mei Wang

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We will provide sufficient conditions for the shifted hypergeometric function z₂F₁(a, b; c; z) to be a member of a specific subclass of starlike functions in terms of the complex parameters a, b and c. For example, we study starlikeness of order α, λ-spirallikeness of order α and strong starlikeness of order α. In particular, those properties lead to univalence of the shifted hypergeometric functions on the unit disk.

Original language	English
Pages (from-to)	1879-1893
Number of pages	15
Journal	Complex Analysis and Operator Theory
Volume	11
Issue number	8
DOIs	https://doi.org/10.1007/s11785-017-0674-4
Publication status	Published - 2017 Dec 1
Externally published	Yes

Keywords

Hypergeometric functions
Spirallike function
Strongly starlike function
Subordination

ASJC Scopus subject areas

Computational Mathematics
Computational Theory and Mathematics
Applied Mathematics

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10.1007/s11785-017-0674-4

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title = "Geometric Properties of the Shifted Hypergeometric Functions",

abstract = "We will provide sufficient conditions for the shifted hypergeometric function z2F1(a, b; c; z) to be a member of a specific subclass of starlike functions in terms of the complex parameters a, b and c. For example, we study starlikeness of order α, λ-spirallikeness of order α and strong starlikeness of order α. In particular, those properties lead to univalence of the shifted hypergeometric functions on the unit disk.",

keywords = "Hypergeometric functions, Spirallike function, Strongly starlike function, Subordination",

author = "Toshiyuki Sugawa and Wang, {Li Mei}",

note = "Publisher Copyright: {\textcopyright} 2017, Springer International Publishing.",

year = "2017",

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doi = "10.1007/s11785-017-0674-4",

language = "English",

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AU - Wang, Li Mei

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N2 - We will provide sufficient conditions for the shifted hypergeometric function z2F1(a, b; c; z) to be a member of a specific subclass of starlike functions in terms of the complex parameters a, b and c. For example, we study starlikeness of order α, λ-spirallikeness of order α and strong starlikeness of order α. In particular, those properties lead to univalence of the shifted hypergeometric functions on the unit disk.

AB - We will provide sufficient conditions for the shifted hypergeometric function z2F1(a, b; c; z) to be a member of a specific subclass of starlike functions in terms of the complex parameters a, b and c. For example, we study starlikeness of order α, λ-spirallikeness of order α and strong starlikeness of order α. In particular, those properties lead to univalence of the shifted hypergeometric functions on the unit disk.

KW - Hypergeometric functions

KW - Spirallike function

KW - Strongly starlike function

KW - Subordination

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JF - Complex Analysis and Operator Theory

SN - 1661-8254

IS - 8

ER -

Geometric Properties of the Shifted Hypergeometric Functions

Abstract

Keywords

ASJC Scopus subject areas

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