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The radius of convexity of normalized Bessel functions

Радиус выпуклости нормализованных функций Бесселя

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Abstract

The radius of convexity of two normalized Bessel functions of the first kind are determined in the case when the order is between -2 and -1. Our methods include the minimum principle for harmonic functions, the Hadamard factorization of some Dini functions, properties of the zeros of Dini functions via Lommel polynomials and some inequalities for complex and real numbers. The results on the zeros of the combination of Bessel functions of the first kind may be of independent interest.

Резюме

Определяется радиус выпуклости двух пормализоваппых фупкциИ Бесселя первого рода в случае, когда их порядок паходится между —2 и -1. Наши методы включают в себя припцип мипимума для гармопических фупкции, факторизацию Лдамара для пекоторых фупкции Дипи, своиства пулеи фупкции Дипи, получеппые с помощью полипомов Ломмеля, и пекоторые перавепства для комплекспых и деиствительпых чисел. Результаты о пулях комбипации фупкции Бесселя первого рода могут представлять самостоятельпьш иптерес.

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Authors and Affiliations

  1. Department of Economics, Babeş-Bolyai University, 400591, Cluj-Napoca, Romania

    Árpád Baricz

  2. Institute of Applied Mathematics, Óbuda University, 1034, Budapest, Hungary

    Árpád Baricz

  3. Department of Mathematics and Informatics, Sapientia Hungarian University of Transylvania, 540485, Târgu-Mureş, Romania

    Róbert Szász

Authors
  1. Árpád Baricz
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  2. Róbert Szász
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Corresponding author

Correspondence to Árpád Baricz.

Additional information

The research of Á. Baricz was supported by a research grant of the Romanian National Authority for Scientific Research, CNCS-UEFISCDI, project number PN-II-RUTE-2012-3-0190.

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Baricz, Á., Szász, R. The radius of convexity of normalized Bessel functions. Anal Math 41, 141–151 (2015). https://doi.org/10.1007/s10476-015-0202-6

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  • DOI: https://doi.org/10.1007/s10476-015-0202-6

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