Abstract
This article attempts to convey an understanding of some of the basic ideas in the proofs of three recent results that deal with successive derivatives of complex analytic functions. These are: (i) if ψ is of order 2, minimal type and lies in the Laguerre-Po1ya class of entire functions, p is a real polynomial, i.e. real on the real axis, and (ϕ = pψ, then ϕ (k) is in the Laguerre-Polya class for all large k.(Craven, Csordas and Smith) (ii) if f is a real entire function of finite order and f, f″ have only real zeros, then f is in the Laguerre-Po1ya class.(Sheil-Small) (iii) if f is a real entire function of order exceeding 2 and its order on the real axis is smaller than its overall order, then each point of the real axis is a limit point of the set of the totality of zeros of f, f′, f″,...(Clunie)
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