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Finite order solutions of second order linear differential equations. (English) Zbl 0669.34010
We consider the differential equation ${f}^{\text{'}\text{'}}+A\left(z\right){f}^{\text{'}}+B\left(z\right)f=0$ where A(z) and B(z) are entire functions. We find conditions on A(z) and B(z) which guarantee that every solution $f¬\equiv 0$ of the equation has infinite order. We also find conditions on A(z) and B(z) which guarantee that any finite order solution $f¬\equiv 0$ of the equation has not zero as a Borel exceptional value. We also show that if A(z) and B(z) satisfy certain growth conditions, then any finite order solution of the equation satisfies certain other growth conditions. Related results are also proven. Several examples are given to complement the theory.
Reviewer: G.G.Gundersen

##### MSC:
 34M99 Differential equations in the complex domain
##### Keywords:
growth conditions; examples