Let z = x+iy. Suppose f(2)=anz is entire. n=0 Prove that if f(z)| ≤ 3|z|ln(|z| +1) Vz, then ƒ is a polynomial. Given con

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Let Z X Iy Suppose F 2 Anz Is Entire N 0 Prove That If F Z 3 Z Ln Z 1 Vz Then F Is A Polynomial Given Con 1 (49.53 KiB) Viewed 33 times

Let z = x+iy. Suppose f(2)=anz is entire. n=0 Prove that if f(z)| ≤ 3|z|ln(|z| +1) Vz, then ƒ is a polynomial. Given concepts: Cauchy's Theorem for Multiply Connected Domains n · fƒ(z)dz = Σf ƒ(2)dz.... Ck k=1 Generalized Cauchy Integral Formula n! f(z) f(n) (zo) = di S -dz 2πi (z − 2₁) n+1² P(x) = 0 when P, Q are polynomials and deg P≤ deg Q - 2 Q(x) Cauchy's Weak Theorem Regularity Theorem Taylor's Theorem Cauchy Inequalities