Estimation of the hyper-order of entire solutions of complex linear ordinary differential equations whose coefficients are entire functions

B. Belaidi, University of Mostaganem, Mostaganem, Algeria

E. J. Qualitative Theory of Diff. Equ., No. 5. (2002), pp. 1-8.

Abstract: We investigate the growth of solutions of the differential equation $f^{\left( n\right) }+A_{n-1}\left( z\right) f^{\left( n-1\right) }+...+A_{1}\left( z\right) f^{^{\prime }}+A_{0}\left( z\right) f=0,$ where $A_{0}\left( z\right) ,...,A_{n-1}\left( z\right) $\ \ are\ entire functions with $A_{0}\left( z\right) \not\equiv 0$. We estimate the hyper-order with respect to the conditions of $A_{0}\left( z\right) ,...,A_{n-1}\left( z\right) $\ if\ $f\not\equiv 0$ has infinite order.

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