Re: Entire function of zero order

On Jul 25, 11:47�am, TCL <tl...@xxxxxxx> wrote:
What is a simple example of a nonpolynomial �entire function that has zero growth rate?

[The growth rate is defined as the lim sup of
(ln ln M(r))/ ln r �as r=|z|--> infinity. Here M(r) is the sup of |f(z)|, |z|=r.]

One of the most interesting classical examples is $f(z) = \sum_{n=0}^
\infty \frac{z^n}{2^{2^n}}$, which has the peculiar property that the
function and all partial sums have only negative real zeros.
.

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