Spirallikeness of shifted hypergeometric functions

Toshiyuki Sugawa, Li Mei Wang

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

In the present paper, we study spirallikenss (including starlikeness) of the shifted hypergeometric function f(z) = z2F1(a, b; c; z) with complex parameters a, b, c, where 2F1(a, b; c; z) stands for the Gaussian hypergeometric function. First, we observe the asymptotic behaviour of 2F1(a, b; c; z) around the point z = 1 to obtain necessary conditions for f to be λ-spirallike for a given λ with -π/2 < λ < π/2. We next give sufficient conditions for f to be λ-spirallike. As special cases, we obtain sufficient conditions of strong starlikeness and examples of spirallike, but not starlike, shifted hypergeometric functions.

Original languageEnglish
Pages (from-to)963-977
Number of pages15
JournalAnnales Academiae Scientiarum Fennicae Mathematica
Volume42
DOIs
Publication statusPublished - 2017

Keywords

  • Cluster set
  • Spirallike function
  • Strongly starlike function

ASJC Scopus subject areas

  • Mathematics(all)

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