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Geometric properties of some Lommel and Struve functions

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Abstract

In this paper our aim is to deduce some new results on the zeros of the derivatives of some Lommel and Struve functions of the first kind and to apply these results in order to determine the radii of convexity of some normalized Lommel and Struve functions of the first kind.

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References

  1. Baricz, Á., Koumandos, S.: Turán type inequalities for some Lommel functions of the first kind. Proc. Edinb. Math. Soc. arXiv:1308.6477 (2014)

  2. Baricz, Á., Szász, R.: The radius of convexity of normalized Bessel functions of the first kind. Anal. Appl. 12(5), 485–509 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  3. Baricz, Á., Szász, R.: Close-to-convexity of some special functions and their derivatives. Bull. Malays. Math. Sci. Soc. arXiv:1402.0692 (2014)

  4. Baricz, Á., Dimitrov, D.K., Mező, I.: Radii of starlikeness and convexity of some \(q\)-Bessel functions. arXiv:1409.0293 (2014)

  5. Baricz, Á., Dimitrov, D.K., Orhan, H., Yağmur, N.: Radii of starlikeness of some special functions. arXiv:1406.3732 (2014)

  6. Baricz, Á., Ponnusamy, S., Singh, S.: Turán type inequalities for Struve functions. arXiv:1401.1430 (2014)

  7. Koumandos, S., Lamprecht, M.: The zeros of certain Lommel functions. Proc. Am. Math. Soc. 140, 3091–3100 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  8. Levin, B.Ya.: Lectures on Entire Functions: Translation of Mathematics Monographs, vol. 150. American Mathematical Society, Providence (1996)

  9. Orhan, H., Yağmur, N.: Geometric properties of generalized Struve functions. An. Ştiinţ. Univ. Al. I. Cuza Ia şi. Mat. (N.S.) (2014)

  10. Pólya, G.: Über die Nullstellen gewisser ganzer Funktionen. Math. Z. 2, 352–383 (1918)

    Article  MATH  Google Scholar 

  11. Skovgaard, H.: On inequalities of the Turán type. Math. Scand. 2, 65–73 (1954)

    Article  MathSciNet  MATH  Google Scholar 

  12. Steinig, J.: The real zeros of Struve’s function. SIAM J. Math. Anal. 1(3), 365–375 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  13. Steinig, J.: The sign of Lommel’s function. Trans. Am. Math. Soc. 163, 123–129 (1972)

    MathSciNet  MATH  Google Scholar 

  14. Watson, G.N.: A Treatise on the Theory of Bessel Functions. Cambridge University Press, Cambridge (1944)

    MATH  Google Scholar 

  15. Yağmur, N., Orhan, H.: Starlikeness and convexity of generalized Struve functions. Abstr. Appl. Anal. 2013: Art. 954513 (2013)

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Acknowledgments

The work of both authors was initiated in September 2014 when they visited the Mathematics Department of Kafkas University in Kars, Turkey. Both authors are grateful to Murat Caǧlar, Erhan Deniz and Nizami Mustafa for their kind hospitality. The authors wish also to thank to the referee for his/her useful comments which enhanced this paper.

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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, Budapest, 1034, Hungary

    Árpád Baricz

  3. Department of Mathematics, Erzincan University, 24000, Erzincan, Turkey

    Nihat Yağmur

Authors
  1. Árpád Baricz
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  2. Nihat Yağmur
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Correspondence to Árpád Baricz.

Additional information

The research of Á. Baricz was supported by the Romanian National Authority for Scientific Research, CNCS-UEFISCDI, under Grant PN-II-RU-TE-2012-3-0190.

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Baricz, Á., Yağmur, N. Geometric properties of some Lommel and Struve functions. Ramanujan J 42, 325–346 (2017). https://doi.org/10.1007/s11139-015-9724-6

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  • DOI: https://doi.org/10.1007/s11139-015-9724-6

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