Radii of Starlikeness and Convexity of a Product and Cross-Product of Bessel Functions

A. Baricz, Anikó Szakál, Róbert Szász, Nihat Yağmur

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

The reality of the zeros of the product and cross-product of Bessel and modified Bessel functions of the first kind is studied. As a consequence the reality of the zeros of two hypergeometric polynomials is obtained together with the number of the Fourier critical points of the normalized forms of the product and cross-product of Bessel functions. As an application some geometric properties of the normalized forms of the cross-product and product of Bessel and modified Bessel functions of the first kind are studied. For the cross-product and the product three different kind of normalization are considered and for each of the six functions tight lower and upper bounds are given for the radii of starlikeness and convexity, via Euler–Rayleigh inequalities. Necessary and sufficient conditions are also given for the parameters such that four from the six normalized functions are convex in the open unit disk.

Original languageEnglish
Article number62
JournalResults in Mathematics
Volume73
Issue number2
DOIs
Publication statusPublished - Jun 1 2018

Fingerprint

Starlikeness
Bessel functions
Cross product
Bessel Functions
Convexity
Radius
Bessel function of the first kind
Modified Bessel Functions
Friedrich Wilhelm Bessel
Hypergeometric Polynomials
Zero
Polynomials
Unit Disk
Normalization
Upper and Lower Bounds
Critical point
Necessary Conditions
Sufficient Conditions
Form

Keywords

  • Bessel and modified Bessel functions of the first kind
  • distribution of zeros of entire functions
  • fourier critical points
  • Laguerre–Pólya class of entire functions
  • radius of starlikeness and convexity
  • zeros of hypergeometric polynomials

ASJC Scopus subject areas

  • Mathematics (miscellaneous)
  • Applied Mathematics

Cite this

Radii of Starlikeness and Convexity of a Product and Cross-Product of Bessel Functions. / Baricz, A.; Szakál, Anikó; Szász, Róbert; Yağmur, Nihat.

In: Results in Mathematics, Vol. 73, No. 2, 62, 01.06.2018.

Research output: Contribution to journalArticle

Baricz, A. ; Szakál, Anikó ; Szász, Róbert ; Yağmur, Nihat. / Radii of Starlikeness and Convexity of a Product and Cross-Product of Bessel Functions. In: Results in Mathematics. 2018 ; Vol. 73, No. 2.
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