ZEROS OF SOLUTIONS OF HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS

We consider the higher order equation f(k) + ak-1,(z)f(k-1) +……+ al(z)f + (Q1(z)ep1(z) + Q2(z)ep2(z) + Q(z))f = 0, where pl(z) = {1zn+’’’ , p2(z) = ’{2zn+’’’ are non constant polynomials, Q1(z)( 0), Q2(z)( 0), Q(z) and aj(z)(j = 1,’’’, k - 1) are entire functions and their orders are less than n. In this paper we treat the case when ’{1/{1 is not real. It is shown that the exponent of convergence to the zero-sequence of any non-trivial solution of the above equation is infinite.