/sci/ - Science & Math

Looks like the other sqt thread was a fake. I am working out of Bak and Newmann's Complex Analysis book and for Proposition 7.3 I do not understand the significance of it and the equation they use to prove it seems out of no where.

Proposition: [math] \text{If f is an entire function satisfying } |f(z)|\leq1/|Imz| \text{for all z, then } f\equiv0 [/math]. They want to estimate [math] |f| \text{on the circle } |z|=R [/math] and they pull this auxiliary function out of their asses [math] g(z)=(z^2-R^2)f(z) [/math]. Any insight would be appreciated.