Ahlfors complex analysis solutions

  • What are the conditions for an analytic function?

    A function f(z) is said to be analytic in a region R of the complex plane if f(z) has a derivative at each point of R and if f(z) is single valued..

  • Analytic Functions
    If f (z) is differentiable and single-valued in a region of the complex plane, it is said to be an analytic function in that region.
  • Definition: A function f is called analytic at a point z0 ∈ C if there exist r \x26gt; 0 such that f is differentiable at every point z ∈ B(z0, r).
    A function is called analytic in an open set U ⊆ C if it is analytic at each point U.
Solution: Suppose first that f(z) is analytic. Let g(z) = f(z). Let uf ,vf and is well-defined and analytic on the complex plane minus x ≤ 0. Hence, the 

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