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Second order differential equations with rational coefficients


Authors: A. Hinkkanen and John Rossi
Journal: Proc. Amer. Math. Soc. 106 (1989), 667-678
MSC: Primary 34A20; Secondary 30D05, 30D35
DOI: https://doi.org/10.1090/S0002-9939-1989-0948151-2
MathSciNet review: 948151
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Abstract: The authors exhibit two linearly independent real solutions, $ {f_1}$ and $ {f_2}$, to $ w'' + Hw = 0$ such that $ {f_1}{f_2}$ is transcendental, $ {f_1}$ and $ {f_2}$ have only real zeros and poles and $ H$ is a nonconstant rational function. This shows the sharpness of a recent result of Hellerstein and Rossi. Some related results are also proved.


References [Enhancements On Off] (What's this?)

  • [1] S. Bank and I. Laine, On the zeros of meromorphic solutions of second-order linear differential equations, Comment Math. Helv. 58 (1983), 656-677. MR 728459 (86a:34008)
  • [2] S. Hellerstein and J. Rossi, Zeros of meromorphic solutions of second order linear differential equations, Math. Z. 192 (1986), 603-612. MR 847009 (87m:34006)
  • [3] E. Hille, Lectures on ordinary differential equations, Addison-Wesley, Reading, Mass., 1969. MR 0249698 (40:2939)
  • [4] E. Ince, Ordinary differential equations, Dover, New York, 1956. MR 0010757 (6:65f)

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DOI: https://doi.org/10.1090/S0002-9939-1989-0948151-2
Article copyright: © Copyright 1989 American Mathematical Society

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