Über den Index der Lösungen Linearer Differentialgieichungen.

In an earliner paper the authors proved the follwoing inequalities for the index (I(r,f) of an entire function f, where λ is the order of f. It is known that the upper bound is sharp. In this paper the authors prove that the lower bound cannot be sharpened if λ≥1 is a rational number. In this direction it is shown that for certain solutions of linear differential equations with polynomial coefficients aj in the left side of the above inequality '≤' and 'lim sup' are replaced by '=' and 'lim'. Also it is proved that the differential equation has constant coefficients if and only if every solution is of bounded index. [ABSTRACT FROM AUTHOR]
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