Normal families and omitted functions II

Let k ⩾ 2 be an integer and let ℱ be a family of functions meromorphic on a domain D in ℂ, all of whose poles are multiple and whose zeros all have multiplicity at least k + 1. Let h be a function meromorphic on D , h ≢ 0, ∞. Suppose that for each f ∈ ℱ, f ( k ) ( z ) ≠ h ( z ) for z ∈ D . Then ℱ is a normal family on D .