Finite order solutions of complex linear differential equations
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We shall consider the growth of solutions of complex linear homogeneous differential equations
ƒ(k) + Ak-1(z) ƒ(k-1) +‧‧‧+ A1(z) ƒ' + A0(z) ƒ = 0
with entire coefficients. If one of the intermediate coefficients in exponentially dominating in a sector and ƒ is of finite order, then a derivative ƒ(j) is asymptotically constant in a slightly smaller sector. We also find conditions on the coefficients to ensure that all transcendental solutions are of infinite order. This paper extends previous results due to Gundersen and to Belaïdi and Hamani.
CitationLaine, I., & Yang, R. (2004). Finite order solutions of complex linear differential equations. Electronic Journal of Differential Equations, 2004(65), pp. 1-8.
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