We show that all non-trivial solutions of complex differential equation \(f''+ A(z)f'+B(z)f = 0\) are of infinite order if coefficients A(z) and B(z) are of special type and establish a relation between the hyper-order of these solutions and the orders of coefficients A(z) and B(z). We have also extended these results to higher order complex differential equations.

中文翻译：

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二阶线性微分方程解的阶和超阶

我们证明，如果系数A（z）和B（z）分别为0，则所有复微分方程\（f''+ A（z）f'+ B（z）f = 0 \）的非平凡解都是无限级的。并在这些解的超序与系数A（z）和B（z）的阶之间建立关系。我们还将这些结果扩展到高阶复微分方程。