# 6. Let f(z) be a function analytic in a region Ω containing z0 an...

## Transcribed Text

6. Let f(z) be a function analytic in a region Ω containing z0 and let fn+1(z) = f(z) − Xn k=0 f (k) (z0) k! (z − z0) k . Show that fn+1(z)(z − z0) n+1 = 1 2πi Z γ f(ζ) dζ (ζ − z0) n+1(ζ − z) , where γ is a any circle |z − z0| = ρ such that the closed disk |z − z0| ≤ ρ is contained in Ω.

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