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  • 1 Óbuda University, 1034 Budapest, Hungary
  • 2 Babeş—Bolyai University, Cluj-Napoca 400591, Romania
  • 3 Society for Electronic Transactions and Security, MGR Knowledge City, CIT Campus, Taramani, Chennai 600113, India
  • 4 Indian Institute of Technology Madras, Chennai 600036, India
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In this paper we deduce some tight Turán type inequalities for Tricomi confluent hypergeometric functions of the second kind, which in some cases improve the existing results in the literature. We also give alternative proofs for some already established Turán type inequalities. Moreover, by using these Turán type inequalities, we deduce some new inequalities for Tricomi confluent hypergeometric functions of the second kind. The key tool in the proof of the Turán type inequalities is an integral representation for a quotient of Tricomi confluent hypergeometric functions, which arises in the study of the infinite divisibility of the Fisher-Snedecor F distribution.

  • [1]

    Abramowitz, M. and Stegun, I. A. (eds.), Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, Dover Publications, New York, 1965.

    • Search Google Scholar
    • Export Citation
  • [2]

    Baricz, Á., Turán type inequalities for generalized complete elliptic integrals, Math. Z., 256(4) (2007), 895911.

  • [3]

    Baricz, Á., Functional inequalities involving Bessel and modified Bessel functions of the first kind, Expo. Math., 26(3) (2008), 279293.

    • Search Google Scholar
    • Export Citation
  • [4]

    Baricz, Á., Turán type inequalities for hypergeometric functions, Proc. Amer. Math. Soc., 136(9) (2008), 32233229.

  • [5]

    Baricz, Á., Turán type inequalities for modified Bessel functions, Bull. Aust. Math. Soc., 82 (2010), 254264.

  • [6]

    Baricz, Á., Turán type inequalities for some probability density functions, Studia Sci. Math. Hung., 47 (2010), 175189.

  • [7]

    Baricz, Á., Bounds for Turánians of modified Bessel functions, Expo. Math., 33(2) (2015), 223251.

  • [8]

    Baricz, Á. and Ismail M. E. H., Turán type inequalities for Tricomi confluent hypergeometric functions, Constr. Approx., 37(2) (2013), 195221.

    • Search Google Scholar
    • Export Citation
  • [9]

    Baricz, Á. and Pogány T. K., Turán determinants of Bessel functions, Forum Math., 26(1) (2011), 295322.

  • [10]

    Baricz, Á. and Ponnusamy, S., On Turán type inequalities for modified Bessel functions, Proc. Amer. Math. Soc., 141(2) (2013), 523532.

    • Search Google Scholar
    • Export Citation
  • [11]

    Barnard, R. W., Gordy, M. B. and Richards, K. C., A note on Turán type and mean inequalities for the Kummer function, J. Math. Anal. Appl., 349(1) (2009), 259263.

    • Search Google Scholar
    • Export Citation
  • [12]

    Craven, T. and Csordas, G., Jensen polynomials and the Turán and Laguerre inequalities, Pacific J. Math., 136(2) (1989), 241260.

  • [13]

    Csordas, G., Norfolk, T. S. and Varga, R. S., The Riemann hypothesis and the Turán inequalities, Trans. Amer. Math. Soc., 296(2) (1986), 521541.

    • Search Google Scholar
    • Export Citation
  • [14]

    Ismail, M. E. H. and Laforgia, A., Monotonicity properties of determinants of special functions, Constr. Approx., 26 (2007), 19.

  • [15]

    Kalmykov, S. I. and Karp, D. B., Log-convexity and log-concavity for series in gamma ratios and applications, J. Math. Anal. Appl., 406(2) (2013), 400418.

    • Search Google Scholar
    • Export Citation
  • [16]

    Kalmykov, S. I. and Karp, D. B., Log-concavity for series in reciprocal gamma functions and applications, Integral Transforms Spec. Funct., 24(11) (2013), 859872.

    • Search Google Scholar
    • Export Citation
  • [17]

    Karp, D. and Sitnik, S. M., Log-convexity and log-concavity of hypergeometriclike functions, J. Math. Anal. Appl., 364(2) (2010), 384394.

    • Search Google Scholar
    • Export Citation
  • [18]

    Koumandos, S. and Pedersen, H. L., Turán type inequalities for the partial sums of the generating functions of Bernoulli and Euler numbers, Math. Nachr., 285 (2012), 21292156.

    • Search Google Scholar
    • Export Citation
  • [19]

    Segura, J., Bounds for ratios of modified Bessel functions and associated Turántype inequalities, J. Math. Anal. Appl., 374(2) (2011), 516528.

    • Search Google Scholar
    • Export Citation
  • [20]

    Simon, T., Produit beta-gamma et regularité du sign, Studia Sci. Math. Hung., 51(4) (2014), 429453.

  • [21]

    Szegő, G., On an inequality of P. Turán concerning Legendre polynomials, Bull. Amer. Math. Soc., 54 (1948), 401405.

  • [22]

    Turán, P., On the zeros of the polynomials of Legendre, Căsopis Pěest. Mat. Fys., 75 (1950), 113122.

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  • Impact Factor (2019): 0.486
  • Scimago Journal Rank (2019): 0.234
  • SJR Hirsch-Index (2019): 23
  • SJR Quartile Score (2019): Q3 Mathematics (miscellaneous)
  • Impact Factor (2018): 0.309
  • Scimago Journal Rank (2018): 0.253
  • SJR Hirsch-Index (2018): 21
  • SJR Quartile Score (2018): Q3 Mathematics (miscellaneous)

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Editor(s)-in-Chief: Pálfy Péter Pál

Managing Editor(s): Sági, Gábor

Editorial Board

  • Biró, András (Number theory)
  • Csáki, Endre (Probability theory and stochastic processes, Statistics)
  • Domokos, Mátyás (Algebra (Ring theory, Invariant theory))
  • Győri, Ervin (Graph and hypergraph theory, Extremal combinatorics, Designs and configurations)
  • O. H. Katona, Gyula (Combinatorics)
  • Márki, László (Algebra (Semigroup theory, Category theory, Ring theory))
  • Némethi, András (Algebraic geometry, Analytic spaces, Analysis on manifolds)
  • Pach, János (Combinatorics, Discrete and computational geometry)
  • Rásonyi, Miklós (Probability theory and stochastic processes, Financial mathematics)
  • Révész, Szilárd Gy. (Analysis (Approximation theory, Potential theory, Harmonic analysis, Functional analysis))
  • Ruzsa, Imre Z. (Number theory)
  • Soukup, Lajos (General topology, Set theory, Model theory, Algebraic logic, Measure and integration)
  • Stipsicz, András (Low dimensional topology and knot theory, Manifolds and cell complexes, Differential topology)
  • Szász, Domokos (Dynamical systems and ergodic theory, Mechanics of particles and systems)
  • Tóth, Géza (Combinatorial geometry)

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