
Complex Analysis Complex Analysis Math Forum 
 LinkBack  Thread Tools  Display Modes 
August 20th, 2014, 04:19 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? 
August 20th, 2014, 07:23 PM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,598 Thanks: 2583 Math Focus: Mainly analysis and algebra 
Have you googled? WA, wikipedia both have articles that give more than you wrote.

August 21st, 2014, 04:52 PM  #3  
Global Moderator Joined: May 2007 Posts: 6,680 Thanks: 658  Quote:
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  

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 06:24 AM 
Analytic continuation  honzik  Complex Analysis  6  May 11th, 2012 04:33 PM 
analytic continuation of an integral involving the mittagle  mmzaj  Complex Analysis  0  February 22nd, 2012 11:37 AM 
a problem on analytic continuation  davedave  Complex Analysis  3  January 16th, 2010 05:33 PM 
Analytic  srw899  Complex Analysis  4  February 27th, 2009 09:10 AM 