Solutions of higher order linear differential equations in an angle

In this paper, we discuss the higher order linear differential equation f(k)+Ak−1f(k−1)+⋯+A1f′+A0f=0f(k)+Ak−1f(k−1)+⋯+A1f′+A0f=0 on an angle. We apply Nevanlinna sectorial theory to estimate the growth of solutions of the equation restricted in the angle and prove the existence of asymptotic value of the derivative of solutions of the equation in the angle. By using these results we can improve some known results in the plane.