On factorization of solutions to second-order homogeneous linear differential equations (Q1886955)

A transcendental meromorphic function \(f(z)\) in the complex plane is said to be factorizable, if \(f(z)=g(h(z))\) with a transcendental meromorphic function \(g(z)\) and a transcendental entire function \(h(z)\). When a factorizable function satisfies a second-order linear differential equation \(f''+A(z)f=0\), the order \(\sigma(f)\) of \(f(z)\) is estimated by using the order \(\sigma(A)\) of \(A(z)\). Some asymptotic properties of such functions are studied.