If a function ,

can we get the conclusion: is a real-analytic function?

(Thinking)

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- October 18th 2009, 07:25 AMXingyuanReal-Analytic Function
If a function ,

can we get the conclusion: is a real-analytic function?

(Thinking) - October 18th 2009, 08:56 AMnimon
No this isn't true. The following example is from 'Loring W. Tu, An Introduction to Manifolds, Springer (2008).'

Consider the function

Then but So the taylor series is in the neighbourhood of the origin, but

The converse is true, however: all analytic functions are on the appropriate domain.