ON THE ZEROS OF THE SOLUTIONS OF Y''+P(Z)Y=0 WHERE P(Z) IS A POLYNOMIAL

Let {z(n)} be the nonzero zeros of the differential equation y'' + P(z)y = 0 , where P(z) = a0 + a1z + a2z2 + - - - + a(N)Z(N), and let c(k) = SIGMA(n = 1)infinity 1/z(n)k for k greater-than-or-equal-to [N/2] + 2. We show that c(k) is a rational function of a(n), n = 0, 1, 2, . .. , N ; futhermore, the successive c(k) can be computed from previous c(k)'s by a simple recurrence relation.