On the Infinite \(\varphi \)-Order Solutions of Second Order Linear Differential Equations

In this paper, we consider the second order linear differential equation where A, B and F with \(B\not \equiv 0\) $B\not\equiv 0$ are entire functions. We find some appropriate conditions on A, B and F in terms of the \(\varphi \) $\phi$ -order which guarantee that every non-constant entire solution f of (†) has infinite \(\varphi \) $\phi$ -order, along with an additional relation between the hyper- \(\varphi \) $\phi$ -order of f and the \(\varphi \) $\phi$ -order of the dominating coefficient in (†).