# Power series

Homework Helper
Gold Member
If I evaluate the power serie

$$y(x) = \sum_{n=0}^{\infty}a_nx^n$$

at x = 0, the first term is $a_0(0)^0$. But 0^0 is undefined, is it not? How is this paradox solved?

Hurkyl
Staff Emeritus
Gold Member
Because that notation for power series doesn't really mean you're supposed to compute 0^0 to get the n=0 term.

Though, some sources will prefer to write that series as

$$y(x) = a_0 + \sum_{n=1}^{\infty}a_nx^n$$

to remove any confusion. (The two mean the same thing, though)

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