On Solution of Second Order Complex Differential Equation

Abstract

In this paper, we establish transcendental entire function $A(z)$ and polynomial $B(z)$ such that the differential equation $f^{\prime \prime }+A(z)f^{\prime }+B(z)f=0$, has all non-trivial solution of infinite order. We use the notion of \emph{critical rays} of the function $e^{P(z)}$, where $A(z)=d(z)e^{P(z)}$ with some restrictions.

8 Pages, Comments are welcome. arXiv admin note: text overlap with arXiv:1809.04516

Cited by in corpus (2)

• Solutions of Higher Order Linear Differential Equations
• [Infinite Order of Growth of Solutions of Second Order Linear Differential Equations