. Use Theorem 1 to establish the Cauchy estimates: n! |f() (zo)| max |f(z), n =...

 

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. Use Theorem 1 to establish the Cauchy estimates: n! |f(") (zo)| max |f(z)\, n = 0, 1, 2, ... |z-zol=r whenever f is analytic on a domain containing the set {z: \z - zol THEOREM 1 Suppose that f is analytic in a domain D and zo is a point of D. If the disc {z: zzo < R} lies in D, then has a power series 00 f(z) = a(z zo)*, k=0 - valid in this disc. Furthermore, the coefficients are given by = 2ni S. f(5) dy (5 - Zo)*+1 where y is the positively oriented circle {5: 15 - z0| = r} and r is any positive number less than R. . Use Theorem 1 to establish the Cauchy estimates: n! |f(") (zo)| max |f(z)\, n = 0, 1, 2, ... |z-zol=r whenever f is analytic on a domain containing the set {z: \z - zol THEOREM 1 Suppose that f is analytic in a domain D and zo is a point of D. If the disc {z: zzo < R} lies in D, then has a power series 00 f(z) = a(z zo)*, k=0 - valid in this disc. Furthermore, the coefficients are given by = 2ni S. f(5) dy (5 - Zo)*+1 where y is the positively oriented circle {5: 15 - z0| = r} and r is any positive number less than R.