.. _sphx_glr_api_gallery_complex_analysis_series:

Series and singularities
------------------------

The behaviour of functions near isolated singularities.


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    <div class="sphx-glr-thumbcontainer" tooltip="An isolated singularity is removable, a pole, or essential, depending on whether the Laurent series has no negative powers, finitely many, or infinitely many. Casorati and Weierstrass showed that near an essential singularity the values of f are dense in the plane. For e^{1/z} at 0 we find a point within \delta = 10^{-3} of 0 where f hits an arbitrary target w, and the phase portrait shows every color packed into every neighbourhood of 0.">

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  :doc:`/api/gallery/complex_analysis/series/plot_01_casorati_weierstrass`

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      <div class="sphx-glr-thumbnail-title">The Casorati-Weierstrass theorem: near an essential singularity f comes close to every value</div>
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   /api/gallery/complex_analysis/series/plot_01_casorati_weierstrass