2. Suppose f is holomorphic in an open set UCC and a E U. Show that for any integern > 0 there is a unique holomorphic function h : U → C such that(z – a)²f(2) = f(a)+f'(a)(z-a)+f"(a)-2!(z – a)²+f(n) (a).+(z-a)"+1h(z), ze U.n!+...

Given f is a holomorphic in an open set U⊂C. Let a∈U. Now, we form a new holomorphic function…

Answered: 2. Suppose f is holomorphic in an open…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.2: Integral Domains And Fields

Problem 24E: If a0 in a field F, prove that for every bF the equation ax=b has a unique solution x in F. [Type...

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2. Suppose f is holomorphic in an open set UC C and a € U. Show that for any integer n ≥ 0 there is a unique holomorphic function h : U → C such that ƒ(z) = f(a)+ƒ'(a)(z−a)+ƒ"(a). (z − a)² 2! (z − a)n n! ·+...+ f(n) (a). -+(z−a)"+¹h(z), z EU.