Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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
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.


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