“…The case m = 0 is already contained in Theorem 1.1, but the present proof is somewhat simpler than that in [32]. The final result is linked to the investigations of [28,30,31,32,33], which in turn followed on from earlier work [18,19,20,21,22,37] concerning the existence of non-real zeros of derivatives of real meromorphic functions in general. It seems likely that if k ≥ 2 and f is a real meromorphic function in the plane, such that f and f (k) have finitely many non-real zeros, then f has in some sense relatively few distinct non-real poles.…”