Fast growing entire solutions of linear differential equations

Анотація

We investigate the fast growing entire solutions of linear differential equations. For that we introduce a general scale to measure the growth of entire functions of infinite order including arbitrary fast growth. We describe growth relations between entire coefficients and  solutions of the linear differential equation $f^{(n)}+a_{n-1}(z)f^{(n-1)}+...+a_{0}(z)f=0$ in this scale. Obtained results contain those for iterated orders as a special case.