## Second order differential equations with transcendental coefficients

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- by John Rossi PDF
- Proc. Amer. Math. Soc.
**97**(1986), 61-66 Request permission

## 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.## References

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*On a problem of Bank and Laine concerning the product of two linear independent solutions to*$y'' + Ay = 0$ (to appear).

## Additional Information

- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**97**(1986), 61-66 - MSC: Primary 30D35; Secondary 34A20
- DOI: https://doi.org/10.1090/S0002-9939-1986-0831388-8
- MathSciNet review: 831388