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Linear differential equations with solutions of finite iterated order. (English) Zbl 0934.34076
The 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 $f''+ A(z) f= 0,$ where $$A(z)$$ is an entire function.

##### MSC:
 34M05 Entire and meromorphic solutions to ordinary differential equations in the complex domain 30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory 34M25 Formal solutions and transform techniques for ordinary differential equations in the complex domain