Uploaded June 2020 | Updated September 2026, 6 hours ago

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Here is a Manim animation of the Taylor serie of the arctangent function up to the order 27 in the 0-neighborhood.
One can clearly see how increasing the order makes a function be numerically closer on the 0-neighborhood. However you can also see each pole appearing far from 0.
It was made with Python and Manim by 3b1b.
The code is available for free here: pastebin.com/ryU9994y