On the zeros ofJν″′(x)

Kokologiannaki, Chrysi G.; Petropoulou, Eugenia N.

doi:10.1080/10652469.2012.720253

Cited by 6 publications

(2 citation statements)

References 19 publications

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“…ν,n − z 2 . On the other hand, we know that ν → j ′′′ ν,n is increasing on (2, ∞) for each n ∈ N fixed (see [14,17]), and thus the function ∞). Consequently, we have that the inequality…”

Section: Proofs Of the Main Resultsmentioning

confidence: 99%

Starlikeness of Bessel functions and their derivatives

Baricz

Çaʇglar

Deni̇z

2016

Mathematical Inequalities &Amp; Applications

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Abstract. In this paper necessary and sufficient conditions are obtained for the starlikeness of Bessel functions of the first kind and their derivatives of the second and third order by using a result of Shah and Trimble about transcendental entire functions with univalent derivatives and Mittag-Leffler expansions for the derivatives of Bessel functions of the first kind, as well as some results on the zeros of these functions.

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Section: Proofs Of the Main Resultsmentioning

confidence: 99%

Starlikeness of Bessel functions and their derivatives

Baricz

Çaʇglar

Deni̇z

2016

Mathematical Inequalities &Amp; Applications

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“…for more details see the papers [13,15] and the references therein. Very recently in 2018, Baricz et al [8] obtained some results for the zeros of the nth derivative of Bessel functions of the first kind for all n ∈ N by using the Laguerre-Pólya class of entire functions and the so-called Laguerre inequalities.…”

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confidence: 99%

Geometric Properties of Bessel function derivatives

Deniz,

Topkaya,

Çağlar

2018

Preprint

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In this paper our aim is to find the radii of starlikeness and convexity of Bessel function derivatives for three different kind of normalization. The key tools in the proof of our main results are the Mittag-Leffler expansion for nth derivative of Bessel function and properties of real zeros of it. In addition, by using the Euler-Rayleigh inequalities we obtain some tight lower and upper bounds for the radii of starlikeness and convexity of order zero for the normalized nth derivative of Bessel function. The main results of the paper are natural extensions of some known results on classical Bessel functions of the first kind.

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