On the kth derivative of meromorphic functions with zeros of multiplicity at least k+1

Abstract

AbstractIn this paper, we prove the following TheoremLet f(z) be a transcendental meromorphic function on C, all of whose zeros have multiplicity at least k+1 (k⩾2), except possibly finitely many, and all of whose poles are multiple, except possibly finitely many, and let the function a(z)=P(z)exp(Q(z))≢0, where P and Q are polynomials such that lim¯r→∞(T(r,a)T(r,f)+T(r,f)T(r,a))=∞. Then the function f(k)(z)−a(z) has infinitely many zeros