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Proceedings of the American Mathematical Society

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

 

 

Second order differential equations with transcendental coefficients


Author: John Rossi
Journal: Proc. Amer. Math. Soc. 97 (1986), 61-66
MSC: Primary 30D35; Secondary 34A20
MathSciNet review: 831388
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Abstract: Let $ {w_1}$ and $ {w_2}$ be two linearly independent solutions to $ w'' + Aw = 0$, where $ A$ is a transcendental entire function of order $ \rho (A) < 1$. We show that the exponent of convergence $ \lambda (E)$ of the zeros of $ E = {w_1}{w_2}$ is either infinite or satisfies $ \rho {(A)^{ - 1}} + \lambda {(E)^{ - 1}} \leq 2$. For $ \rho (A) = \tfrac{1}{2}$, this answers a question of Bank.


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DOI: https://doi.org/10.1090/S0002-9939-1986-0831388-8
Article copyright: © Copyright 1986 American Mathematical Society