Tuesday, 1 October 2013

Zeros of a power series

Zeros of a power series

Suppose we have a power series with (real or complex) coefficients
$\sum_{n \geq 0} a_n x^n$ (that has nonzero radius of convergence). Can
one say something about its zeros in terms of the coefficients $\{ a_n
\}_{n \geq 0}$?
In general, what are the methods of finding zeros of a power series? Are
there any?

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