Close-to-Convexity of Some Special Functions and Their Derivatives

A. Baricz, Róbert Szász

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

In this paper our aim is to deduce some sufficient (and necessary) conditions for the close-to-convexity of some special functions and their derivatives, like Bessel functions, Struve functions, and a particular case of Lommel functions of the first kind, which can be expressed in terms of the hypergeometric function $${}_1F_2$$1F2. The key tool in our proofs is a result of Shah and Trimble about transcendental entire functions with univalent derivatives. Moreover, a known result of Pólya on entire functions, the infinite product representations and some results on zeros of Bessel, Struve, and Lommel functions of the first kind are used in order to achieve the main results of the paper.

Original languageEnglish
Pages (from-to)427-437
Number of pages11
JournalBulletin of the Malaysian Mathematical Sciences Society
Volume39
Issue number1
DOIs
Publication statusPublished - Jan 1 2016

Fingerprint

Special Functions
Convexity
Derivative
Entire Function
Transcendental function
Infinite product
Hypergeometric Functions
Friedrich Wilhelm Bessel
Bessel Functions
Deduce
Necessary Conditions
Sufficient Conditions
Zero

Keywords

  • Bessel functions of the first kind
  • Close-to-convex functions
  • Entire functions
  • Lommel functions of the first kind
  • Struve functions
  • Zeros of Bessel, Lommel and Struve functions

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Close-to-Convexity of Some Special Functions and Their Derivatives. / Baricz, A.; Szász, Róbert.

In: Bulletin of the Malaysian Mathematical Sciences Society, Vol. 39, No. 1, 01.01.2016, p. 427-437.

Research output: Contribution to journalArticle

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