Fast growing entire solutions of linear differential equations

Igor Chyzhykov, Nadiya Semochko


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.

Ключові слова

linear differential equation, entire function, growth of solutions, Nevanlinna characteristic, iterated order

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