My Math Forum Holomorphic annulus example

 Complex Analysis Complex Analysis Math Forum

 February 25th, 2018, 06:19 AM #1 Senior Member   Joined: Jan 2016 From: Blackpool Posts: 104 Thanks: 2 Holomorphic annulus example let 0
 February 25th, 2018, 06:45 AM #2 Senior Member   Joined: Jan 2016 From: Blackpool Posts: 104 Thanks: 2 edit: we know that the prinicipal branch is holomorphic unless z is real and non positive. So if we express z in rectangular form z=x+iy when y=0 we have z=x where z is not holomorphic when x is less than 0. Therefore no matter how small you choose the annulus with centre 0, and 0
February 25th, 2018, 04:14 PM   #3
Senior Member

Joined: Sep 2016
From: USA

Posts: 628
Thanks: 398

Math Focus: Dynamical systems, analytic function theory, numerics
Quote:
 Originally Posted by Jaket1 edit: we know that the prinicipal branch is holomorphic unless z is real and non positive. So if we express z in rectangular form z=x+iy when y=0 we have z=x where z is not holomorphic when x is less than 0. Therefore no matter how small you choose the annulus with centre 0, and 0
This doesn't really work since the claim "log is not holomorphic" is exactly what this question is asking you to prove. Try computing a line integral for 1/z and applying Cauchy's theorem.

 Tags annulus, holomorphic

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post Jaket1 Complex Analysis 1 January 26th, 2018 06:33 AM Happy Calculus 3 December 15th, 2014 03:06 AM Seijo Complex Analysis 0 September 11th, 2012 04:11 PM JamesKirk Complex Analysis 0 January 29th, 2012 11:52 AM alpar_r Complex Analysis 3 October 27th, 2010 01:40 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top