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Taylor and Laurent series

Click anywhere to choose a center z₀. The function f(z) = 1/((z−1)(z−2)) has three series about z₀, valid on three regions set by the two poles (×): a Taylor disc, a Laurent annulus, and a Laurent exterior.

A modern JavaScript + Canvas port of a Java applet by Terence Tao (~2007, originally LaurentApp.java / LaurentGrid.java).

Taylor series

Laurent series (annulus)

Laurent series (exterior)