Practice problem
Let f(z)=z−1f(z) = z^{-1}f(z)=z−1 for z≠0z\neq0z=0. Describe the function g(z)=12πi∮∣ζ∣=1dζf(ζ)ζ−zg(z) = \frac{1}{2\pi i}\oint_{\lvert \zeta\rvert = 1} d\zeta\frac{f(\zeta)}{\zeta - z}g(z)=2πi1∮∣ζ∣=1dζζ−zf(ζ) for inputs zzz in the open unit disk ∣z∣<1\lvert z \rvert < 1∣z∣<1.
ggg is undefined at 000, but g(z)=f(z)g(z) = f(z)g(z)=f(z) for z≠0z\neq0z=0.
g(0)=0g(0) = 0g(0)=0 and g(z)=f(z)g(z) = f(z)g(z)=f(z) for z≠0z\neq0z=0.
ggg is undefined at 000, but g(z)=0g(z) = 0g(z)=0 for z≠0z\neq0z=0.
g(z)=0g(z) = 0g(z)=0, whether z=0z=0z=0 or z≠0z\neq0z=0.
Type a concept, like “slope” or “photosynthesis”.