I am trying assignment in complex analysis of an institute in which I don't study because the instructor who taught me was terrible didn't bothered to give any assignment and also was poor in teaching concepts . So , I try problems of a different institute .
Question : If $f :\mathbb{C} \to \mathbb{C}$ has a power series expansion around each point then does it have a single power series expansion valid on all of $\mathbb{C}$ ?
If $f :\mathbb{R} \to \mathbb{R}$ has a power series expansion around each point then does it have a single power series expansion valid on all of $\mathbb{R}$ ?
I have no clue on which concept should be used . Kindly tell what concepts / results should be used give a hint or two (if necessary) and rest I would like to work by myself .
Thanks!!