#
Taylor and Laurent expansions

This applet displays the various Taylor and Laurent expansions of the function
`f(z) = 1/(z-1)(z-2)`. At each point `z_0`, the function
`f` has a Taylor expansion around `z_0`, which converges
in the red disk; a Laurent expansion around `z_0`, which converges
in the green annulus; and a second Laurent expansion around `z_0`,
which converges in the cyan disk exterior. Note that there are some
white circles for which none of the three series converge; these include
the singularities of `f` at 1 and 2. Click on the grid to
move the point `z_0`.
To read off all the displayed terms of a Taylor or Laurent series, one
may have to use the cursor keys to navigate the text windows.

Note that the co-efficients of the Taylor series become much larger
as one approaches a singularity.

Thanks to Brandt Kronholm for pointing out an error in an earlier version of this applet.

Previous applet: The complex integral

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