“…Extensive research into the non-real zeros of derivatives of real entire functions [2,3,4,5,7,16,17,23,24,25,35,38] arose largely from the conjecture of Wiman (now proved in [3,35,38]) that if f is a real entire function such that f and f ′′ have only real zeros, then f belongs to the Laguerre-Pólya class consisting of locally uniform limits of real polynomials with real zeros, as well as from related conjectures of Pólya [36]. The starting point of the present paper is the analogous problem where f , rather than being entire, is the reciprocal of a real entire function with real zeros.…”