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

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• 作者：Árpád Baricz ; Róbert Szász
• 关键词：Bessel functions of the first kind ; Lommel functions of the first kind ; Struve functions ; Close ; to ; convex functions ; Entire functions ; Zeros of Bessel ; Lommel and Struve functions ; 33C10 ; 30C45
• 刊名：Bulletin of the Malaysian Mathematical Sciences Society
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：39
• 期：1
• 页码：427-437
• 全文大小：431 KB
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  4.Baricz, Á., Koumandos, S.: Turán type inequalities for some Lommel functions of the first kind. Proc. Edinb. Math. Soc. (2014) (in press)
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  19.Szász, R.: On starlikeness of Bessel functions of the first kind. In: Proceedings of the 8th Joint Conference on Mathematics and Computer Science, Komárno, Slovakia (2010)
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• 作者单位：Árpád Baricz (1)
  Róbert Szász (2)
  
  1. Department of Economics, Babeş-Bolyai University, 400591, Cluj-Napoca, Romania
  2. Department of Mathematics and Informatics, Sapientia Hungarian University of Transylvania, 540485, Târgu-Mureş, Romania
  
• 刊物类别：Mathematics, general; Applications of Mathematics;
• 刊物主题：Mathematics, general; Applications of Mathematics;
• 出版者：Springer Singapore
• ISSN：2180-4206

文摘

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 \({}_1F_2\). 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. Keywords Bessel functions of the first kind Lommel functions of the first kind Struve functions Close-to-convex functions Entire functions Zeros of Bessel, Lommel and Struve functions