Editing Isolated singularity (section)

===Examples===
[[Image:Natural_boundary_example.gif|thumb|right|256px|The natural boundary of this power series is the unit circle (read examples).]]
*The function <math display="inline">\tan\left(\frac{1}{z}\right)</math> is [[meromorphic]] on <math>\mathbb{C}\setminus\{0\}</math>, with simple poles at <math display="inline">z_n = \left(\frac{\pi}{2}+n\pi\right)^{-1}</math>, for every <math> n\in\mathbb{N}_0</math>. Since <math>z_n\rightarrow 0</math>, every punctured disk centered at <math>0</math> has an infinite number of singularities within, so no Laurent expansion is available for <math display="inline">\tan\left(\frac{1}{z}\right)</math> around <math>0</math>, which is in fact a cluster point of its poles.
*The function <math display="inline">\csc \left(\frac {\pi} {z}\right)</math> has a singularity at 0 which is ''not'' isolated, since there are additional singularities at the [[Multiplicative inverse|reciprocal]] of every [[integer]], which are located arbitrarily close to 0 (though the singularities at these reciprocals are themselves isolated).
*The function defined via the [[Maclaurin series]] <math display="inline">\sum_{n=0}^{\infty}z^{2^n}</math> converges inside the open unit disk centred at <math>0</math> and has the unit circle as its natural boundary.