AURENT ’ STCF

Consider the function f : C \ {2} → C given by f (z) = 1z−2 . By Taylor’s theorem, f has a Taylor series centered at z0 = 0 with neighborhood of convergenceN2(0). That is,

f (z) = ∞∑ j=0

f (j)(0)

j! zj on N2(0).