On the zeros of generalized Airy functions

  • Àrpàd Elbert
  • Andrea Laforgia
Original Papers


We investigate the behaviour with respect to the parameterγ > 0 of the zeros of the solutions of the differential equation y+yγ=0. We show that under appropriate restrictions such zeros are logconvex.


Differential Equation Mathematical Method Airy Function Generalize Airy Function 
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  1. [1]
    C. Comstock, Onweighted averages at a jump discontinuity, Quart. Appl. Math.28, 159–166 (1970).Google Scholar
  2. [2]
    Á. Elbert, A. Laforgia and L. Lorch,Additional monotonicity properties of the zeros of Bessel functions, Analysis (to appear).Google Scholar
  3. [3]
    L. Gatteschi and A. Laforgia,Nuove disuguaglianze per il primo zero ed il primo massimo délla funzione di Bessel j v(x). Rend. Sem. Mat. Univ. Pol. Torino,34, 411–424 (1975–76).Google Scholar
  4. [4]
    A. Laforgia and M. E. Muldoon,Monotonicitv properties of zeros of generalized Airy functions, Z. angew. Math. Phys. (ZAMP),39, 267–271 (1988).Google Scholar
  5. [5]
    L. N. Nosova and S. A. Tumarkin,Tables of Generalized Airy Functions for the Asymptotic Solution of the Differential Equations, translated by D. E. Brown, Pergamon/McMillan, Oxford 1965 (Russian original, Computing Centre of the Academy of Sciences of the USSR, Moscow, 1961).Google Scholar
  6. [6]
    A. D. Smirnov,Tables of Airy Functions and Special Confluent Hypergeometric Functions for Asymptotic Solutions of Differential Equations of the Second Order, translated from the Russian by D. G. Fry, Pergamon, Oxford 1960.Google Scholar
  7. [7]
    R. Spigler,Alcuni risultati sugli zeri delle funzioni cilindriche e delle loro derivate, Rend. Sem. Mat. Univ. Pol. Torino,38, 67–85 (1980).Google Scholar
  8. [8]
    C. A. Swanson and V. B. Headley,An extension of Airy's equation, SIAM J. Appl. Math.15, 1400–1412 (1967).Google Scholar
  9. [9]
    G. N. Watson,A Treatise on the Theory of Bessel Functions, 2nd ed. Cambridge University Press 1944.Google Scholar

Copyright information

© Birkhäuser Verlag 1991

Authors and Affiliations

  • Àrpàd Elbert
    • 1
  • Andrea Laforgia
    • 2
  1. 1.Mathematical Institute of the Hungarian Academy of SciencesBudapestHungary
  2. 2.Dipartimento di EnergeticaUniversità degli Studi di L'AquilaRoioItaly

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