Li Songying
In this paper, we shall prove the existence of the singular directions related to Hayman's problems
[1]. The results are as follows.Suppose that f(z) is a transcendental integral function in the finite plane, then there exists a direction H: arg
z= θ
0 (0≤θ
0>2π) ε, every integer p(≠0, -1) and every finite complex number b(≠0), we have
} \right\} = + \infty $$)
Suppose that f(z) is a transcendental integral function in the finite plane, then there exists a direction H:
z= θ
0 (0≤θ
0>2π) ε, every integrer p(≥3) and any finite complex numbers a(≠0) and b, we have
} \right\} = + \infty $$)
Suppose that f(z) is a meromorphic function in the finite plane and satisfies the following condition
}}{{(\log r)^3 }} = + \infty $$)
then there exists a direction H:
z= θ
0 (0≤θ
0>2π) ε, every integer p(≥5) and every two finite complex numbers a(≠0) and b, we have
The singular directions in Theorems Ⅰ-Ⅲ are called Hayman directions.
