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Show that the multivalued-function $sqrt{z^2-25}$ has an analytic branch in the domain $Bbb Csetminus D(0,5)$

Analytic in the domainFind a branch of $f(z)= log(z^3-2)$ that is analytic at $z=0$.Find a branch of the multiple-valued function $(4+z^2)^{frac{1}{2}}$ that is analytic in the given domain $D$ whereFind a branch of $log (2z - 1)$ that is analytic at all points in the planesingle valued analytic branch of multivalued functionProve a function is a branch of another multivalued functionWhat should be the choice of arguments of the branch cuts of multivalued complex functions..Image of an analytic function near a branch pointShow the function is analyticAnalytic multi-valued function: Can multi-valued functions be analytic without choosing a cut of the domain?

-1

$begingroup$

Can someone help me show that the multi-valued function $sqrt{z^2 − 25}$ has an analytic branch in the domain D$ = Bbb C setminus D(0, 5)$?

complex-analysis

share|cite|improve this question

edited Mar 14 at 13:07

Daniele Tampieri

2,5772922

asked Mar 14 at 12:36

Emma Lorenzo CasasEmma Lorenzo Casas

11

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  D(0,5) is? Closed disk around 0 of radius 5?
  $endgroup$
  – Calvin Khor
  Mar 14 at 13:18
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Yes, closed disk around 0 of radius 5
  $endgroup$
  – Emma Lorenzo Casas
  Mar 14 at 13:23
  

  
  
  
  

add a comment | 

-1

$begingroup$

Can someone help me show that the multi-valued function $sqrt{z^2 − 25}$ has an analytic branch in the domain D$ = Bbb C setminus D(0, 5)$?

complex-analysis

share|cite|improve this question

edited Mar 14 at 13:07

Daniele Tampieri

2,5772922

asked Mar 14 at 12:36

Emma Lorenzo CasasEmma Lorenzo Casas

11

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  D(0,5) is? Closed disk around 0 of radius 5?
  $endgroup$
  – Calvin Khor
  Mar 14 at 13:18
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Yes, closed disk around 0 of radius 5
  $endgroup$
  – Emma Lorenzo Casas
  Mar 14 at 13:23
  

  
  
  
  

add a comment | 

$begingroup$

Can someone help me show that the multi-valued function $sqrt{z^2 − 25}$ has an analytic branch in the domain D$ = Bbb C setminus D(0, 5)$?

complex-analysis

share|cite|improve this question

edited Mar 14 at 13:07

Daniele Tampieri

2,5772922

asked Mar 14 at 12:36

Emma Lorenzo CasasEmma Lorenzo Casas

11

$endgroup$

share|cite|improve this question

edited Mar 14 at 13:07

Daniele Tampieri

2,5772922

asked Mar 14 at 12:36

Emma Lorenzo CasasEmma Lorenzo Casas

11

share|cite|improve this question

edited Mar 14 at 13:07

Daniele Tampieri

2,5772922

asked Mar 14 at 12:36

Emma Lorenzo CasasEmma Lorenzo Casas

11

edited Mar 14 at 13:07

Daniele Tampieri

2,5772922

edited Mar 14 at 13:07

Daniele Tampieri

2,5772922

asked Mar 14 at 12:36

Emma Lorenzo CasasEmma Lorenzo Casas

11

asked Mar 14 at 12:36

Emma Lorenzo CasasEmma Lorenzo Casas

11