Can there be more than one power series expansion for a function. I guess the answer is NO, for polynomials.
I know that there are more than one series expansion for every function.
But I am talking about power series here.
All Ideas are appreciated 

Two different power series (around the same point) cannot converge to the same function.
If the power series both have positive radius of convergence, and their $n$th coefficients differ, then the $n$th derivatives of the functions they define also differs, so they cannot be the same function.
