Taylors Therory

[manjunathan]

suppose a function is analytic in open set U and z 0 is point of U open disk delta =delta of z0,R is contained in U then f can be represented in delta as the sum of tyalor series around the point z0

 

[DrPhil]

suppose a function is analytic in open set U and z 0 is point of U open disk delta =delta of z0,R is contained in U then f can be represented in delta as the sum of tyalor series around the point z0

What is the Question, please?

 

[HallsofIvy]

suppose a function is analytic in open set U and z 0 is point of U open disk delta =delta of z0,R is contained in U then f can be represented in delta as the sum of tyalor series around the point z0

That is simply a restatement of the definition of "analytic". Do you have a question about it?

 

[daon2]

"Analytic on U" could have been defined as "differentiable on U", and the question as I read it is asking for a proof that it may be represented as a series in a disk about z_0

 

[HallsofIvy]

Possibly, but there several other equivalent definitions of "analytic". We cannot be certain which definition manjunathan is using until he comes back to tell us.