一类整函数的奇异方向

The Singular Directions for a Classe of Entire Functions

设 f ( z)为ρ( q)级的整函数 ,则存在一奇异方向Δ:arg z =θ0 ,具有性质 :若 m,k,l为 3个正整数 ,满足 m +1k +1l <1 ,则对任意ε>0 ,任意有穷复数α和有穷非零复数β,有limr→ +∞ln [nk-1) ( r,θ0 ,ε,f =α) +nl+ 1) ( r,θ0 ,ε,f(m) =β) ]( ln) q r =ρ( q) .

Let f(z) be an entire function of order ρ(q),then exists a singular direction Δ:argθ 0,such that if m,k,l are positive integers satisfying m+1k+1l<1, for any ε>0,and any finite complex number α and any finite non zero complex number β,hase limr→+∞ln[n k-1)(r,θ 0,ε,f=α)+n l+1)(r,θ 0,ε,f (m)=β)](ln) q r=ρ(q).