Let f(z) be holomorphic on |z| < 2. Let n 1 be a natural number....

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Let f(z) be holomorphic on |z| < 2. Let n ≥ 1 be a natural number. For any z with |z| < 1 let 1 f(5). zn g(z) = f(z) — - -ds 2πi |2|=1 (5-2) 5n Prove that g(z) is a polynomial of degree at most n. Hint: Expand (5-2)n into partial fractions as a function of C. You only need to compute one of the coefficients in the partial fractions expansion. Let f(z) be holomorphic on |z| < 2. Let n ≥ 1 be a natural number. For any z with |z| < 1 let 1 f(5). zn g(z) = f(z) — - -ds 2πi |2|=1 (5-2) 5n Prove that g(z) is a polynomial of degree at most n. Hint: Expand (5-2)n into partial fractions as a function of C. You only need to compute one of the coefficients in the partial fractions expansion.