My Math Forum  

Go Back   My Math Forum > College Math Forum > Complex Analysis

Complex Analysis Complex Analysis Math Forum


Thanks Tree2Thanks
  • 1 Post By v8archie
  • 1 Post By mathman
Reply
 
LinkBack Thread Tools Display Modes
August 20th, 2014, 03:19 PM   #1
Senior Member
 
Joined: Aug 2014
From: United States

Posts: 137
Thanks: 21

Math Focus: Learning
Understanding Analytic Continuation

Can somebody help me to further increase my understanding of analytic continuation and its applications?

At this point I understand that analytic continuation is a method of increasing the domain of a complex function.

I also know that if two functions, say $f$ and $g$, are analytic on two domains, say $\Omega_f$ and $\Omega_g$ respectively, where $f=g$ on the domain $\Omega_f\cap\Omega_g$, then $g$ is an analytic continuation of $f$.

Is this correct?

And also, what is this used for, and what's it got to do with the Riemann Zeta Function?
neelmodi is offline  
 
August 20th, 2014, 06:23 PM   #2
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 7,635
Thanks: 2620

Math Focus: Mainly analysis and algebra
Have you googled? WA, wikipedia both have articles that give more than you wrote.
Thanks from neelmodi
v8archie is offline  
August 21st, 2014, 03:52 PM   #3
Global Moderator
 
Joined: May 2007

Posts: 6,730
Thanks: 689

Quote:
Originally Posted by neelmodi View Post
Can somebody help me to further increase my understanding of analytic continuation and its applications?

At this point I understand that analytic continuation is a method of increasing the domain of a complex function.

I also know that if two functions, say $f$ and $g$, are analytic on two domains, say $\Omega_f$ and $\Omega_g$ respectively, where $f=g$ on the domain $\Omega_f\cap\Omega_g$, then $g$ is an analytic continuation of $f$.

Is this correct?

And also, what is this used for, and what's it got to do with the Riemann Zeta Function?
You need some restriction on $\Omega_f\cap\Omega_g$, such as containing an open set.

The infinite series for the Zeta function converges only for Re(s) > 1. Continuation allows it to be extended to the whole complex plane, except for pole at s=1.

Riemann zeta function - Wikipedia, the free encyclopedia
Thanks from neelmodi
mathman is offline  
Reply

  My Math Forum > College Math Forum > Complex Analysis

Tags
analytic, continuation, understanding



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Analytic??? GgiPunjab Number Theory 1 January 8th, 2013 05:24 AM
Analytic continuation honzik Complex Analysis 6 May 11th, 2012 03:33 PM
analytic continuation of an integral involving the mittag-le mmzaj Complex Analysis 0 February 22nd, 2012 10:37 AM
a problem on analytic continuation davedave Complex Analysis 3 January 16th, 2010 04:33 PM
Analytic srw899 Complex Analysis 4 February 27th, 2009 08:10 AM





Copyright © 2019 My Math Forum. All rights reserved.