# On the Zero Distribution of Solutions of Second Order Linear Differential Equations in the Complex Domain

### From NZJM

**New Zealand Journal of Mathematics**

**Vol.** 42, (2012), **Pages** 9-16

**Jianren Long **

School of Mathematics and Computer Science,

Guizhou Normal University,

Guiyang, 550001, P. R. China

mailto:longjianren2004@163.com

**Pengcheng Wu**

School of Mathematics and Computer Science,

Guizhou Normal University,

Guiyang, 550001, P. R. China

**Xiubi Wu**

School of Mathematics and Computer Science,

Guizhou Normal University,

Guiyang, 550001, P. R. China

**Abstract** Let be a solution of *f*'' + *P*(*z*)*f* = 0, where *P*(*z*) is a polynomial. Then the set of accumulation lines of zero-sequence is a subset of the
Borel directions of *f*(*z*). Let *f*_{1} and *f*_{2} be two linearly
independent solutions of *f*'' + *P*(*z*)*f* = 0, where *P*(*z*) is a polynomial of degree *n* and set *E* = *f*_{1}*f*_{2}. Then, for every accumulation line of zero-sequence of *E*, there is another accumulation line of zero-sequence of *E* such that .

**Keywords** Differential equation, accumulation line of zero-sequence, exponent of convergence of zero-sequence, angular distribution.

**Classification** (MSC2000) 34M10; 30D35.