The rate of growth of solutions of linear differential equations with meromorphic coefficients (Q874847)

The hyper-order \(\sigma_2(f)\) of a meromorphic function \(f(z)\) is defined by the upper limit of\break \(\log\log T(r,f)/\log r\). When a meromorphic function \(f(z)\) satisfies a linear ordinary differential equation with meromorphic coefficients, \(\sigma_2(f)\) is evaluated by using the orders \(\sigma(A_j)\) of the coefficients \(A_j\) of the differential equation. This is a generalization of the result in [\textit{Z.-X. Chen}, Kodai Math. J., 22, 208--221 (1999; Zbl 0940.34069)] where \(f\) satisfies a second order differential equation.