无穷级亚纯函数的T方向和Borel方向

T Direction and Borel Direction of Meromorphic Functions of Infinite Order

对任意正整数q1和q2,记E1={argz=θj|0≤θ1<θ2<…<θq1<2π}及E2={argz=φj|0≤φ1<φ2<…<φq2<2π},若E1∩E2=Φ.则(i)对任意正整数μ,存在复平面上下级为μ的无穷级亚纯函数f(z),恰以E1∪E2为其T方向且恰以E1为其Borel方向.(ii)存在复平面上的下级为无穷的亚纯函数f(z),恰以E1∪E2为其Borel方向且恰以E1为其T方向.

Let q1 and q2 be any positive integers. Assume that E1={argz=θj｜0≤θ1〈θ2〈…〈θq1〈2π} E2={argz=φj｜0≤φ1〈φ2〈…〈φq2〈2π} such that E1 ∩ E2 =φ. Then （1） for any positive number μ, there exists a meromorphic function f（z） of lower order μ and infinite order, which takes the E1 ∪ E2 as its T direction and E1 as its Borel derection.（2） there exists a meromorphic function f（z） of infinite lower order, which takes the E1 ∪ E2 as its Borel direction and E1 as its T direction.