Second Order Differential Equations with Rational Coefficients

Abstract

Abstract.The authors exhibit two linearly independent real solutions, f\ and fi, to w" + Hw = 0 such that /1/2 is transcendental, f and fi have only real zeros and poles and H is a nonconstant rational function. This shows the sharpness of a recent result of Hellerstein and Rossi. Some related results are also proved.