ON THE GROWTH OF SOLUTIONS OF CERTAIN LINEAR-DIFFERENTIAL EQUATIONS

Suppose g(j), 0 less-than-or-equal-to j less-than-or-equal-to n - 1, and h are entire functions and that for some k, 0 less-than-or-equal-to k less-than-or-equal-to n - 1/2, the order of g(k) does not exceed 1/2 and does exceed the order of h and the order of all other g(j) . It is shown that then every solution of the differential equation [GRAPHICS] is either a polynomial or an entire function of infinite order. This generalizes a previous result of the authors for second order equations.