There exists an entire function F with the following “universal” property: given
uniformly on every compact subset of C.
(a) Let p1, p2,… denote an enumeration of the collection of polynomials whose coefficients have rational real and imaginary parts. Show that it suffices to find an entire function F and an increasing sequence {Mn} of positive integers, such that
(b) Construct F satisfying (17) as an infinite series
uniformly on every compact subset of C. Here DjG denotes the jth (complex) derivative of G.
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