The Growth of Solutions to Higher Order Differential Equations with Exponential Polynomials as Its Coefficients

By looking at the situation when the coefficients P j ( z ) ( j = 1, 2, ⋯, n − 1) (or most of them) are exponential polynomials, we investigate the fact that all nontrivial solutions to higher order differential equations f ( n ) + P n −1 ( z ) f (n − 1) + ⋯ + P 0 ( z ) f = 0 are of infinite order. An exponential polynomial coefficient plays a key role in these results.