Linear differential equations with solutions of finite iterated order.

*(English)*Zbl 0934.34076The author deals with complex homogeneous and nonhomogeneous linear differential equations with coefficients of finite iterated order. Several results are presented concerning the iterated order of solutions and the iterated convergence exponent of the zeros of solutions. Special attention is paid to the second-order case

$${f}^{\text{'}\text{'}}+A\left(z\right)f=0,$$

where $A\left(z\right)$ is an entire function.

Reviewer: J.Saurer (Regensburg)

##### MSC:

34M05 | Entire and meromorphic solutions (ODE) |

30D35 | Distribution of values (one complex variable); Nevanlinna theory |

34M25 | Formal solutions, transform techniques (ODE in the complex domain) |