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Suppose f: C → C is a holomorphic function. Let g(z) = ƒ(₹). Using the Cauchy Riemann equations, or otherwise, show that g is holomorphic on C.

Suppose f: C → C is a holomorphic function. Let g(z) = ƒ(₹). Using the Cauchy Riemann equations, or otherwise, show that g is holomorphic on C.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**4.** Suppose \( f: \mathbb{C} \to \mathbb{C} \) is a holomorphic function. Let \( g(z) = \overline{f(\overline{z})} \). Using the Cauchy–Riemann equations, or otherwise, show that \( g \) is holomorphic on \( \mathbb{C} \).
Transcribed Image Text:**4.** Suppose \( f: \mathbb{C} \to \mathbb{C} \) is a holomorphic function. Let \( g(z) = \overline{f(\overline{z})} \). Using the Cauchy–Riemann equations, or otherwise, show that \( g \) is holomorphic on \( \mathbb{C} \).
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