关于线性微分多项式的一个亏量关系

A deficiency relation for linear differential polynomials

下面亏量关系得到证明:设f是一超越亚纯函数,D[f]是f的一个k (k≥1)阶线性微分多项式,且超越亚纯.如果微分方程(D[ω]) =0的每一亚纯解ω都是(D[f]) 的小函数,则 a≠∞δ(a,D[f])<1+12k+1,这里是对一切有穷复数a求和.

The following deficiency relation is shown:Let f be a transendental meromorphic function,and D[f] be a k th-order linear differential polynomial of f.If any ω,meromorphic solution of the differential equation (D[ω])'=0, is a small function of (D[f])', then for all a∈C,there existsa≠∞δ(a,D[f])<1+12k+1.