单位圆内无穷级亚纯函数的T-半径和Borel半径

T-Radii and Borel Radii of Meromorphic Functions of Infinite Order in the Unit Disc

设E1=argz=θj|0≤θ1<θ2<…<θq1<2π,E2=argz=φj0≤φ1<φ2<…<φq2<2π,且E1∩E2=Φ,q1和q2是任意正整数.证明了(1)存在Δ内下级为任一正数的无穷级亚纯函数f(z),恰以E1∪E2为其T-半径且恰以E2为其Borel半径;(2)存在Δ内下级为无穷的亚纯函数g(z),恰以E1∪E2为其Borel半径且恰以E2为其T-半径.

LetE1=arg z=θj0≤θ1θ2…θq12πE2=arg z=φj0≤φ1φ2…φq22πsuch that E1∩E2=,and q1 and q2 be positive integers.Then （1） there exists a meromorphic function f（z） of infinite order and finite positive lower order in,which takes the E1∪E2 as its T-radii and E2 as its Borel radii,（2） there exists a meromorphic function g（z） of infinite lower order in,which takes the E1∪E2 as its Borel radii and E2 as its T-radii.