# [SOLVED]power series

#### dwsmith

##### Well-known member
What would be the power series of $g(t)$?

$$g(t) = \sum_{n=0}^{\infty}\frac{g(t)}{n!}$$

This?

#### tkhunny

##### Well-known member
MHB Math Helper
?? What EXACTLY are you trying to do? I'm guessing the recursive definition you have suggested is not a good way to go.

#### CaptainBlack

##### Well-known member
What would be the power series of $g(t)$?

$$g(t) = \sum_{n=0}^{\infty}\frac{g(t)}{n!}$$

This?
There is a mistake in your post, as posted there is no such function other than the zero function.

CB

#### Fantini

The power series of a function around a point $$t_0$$ is $$g(t) = \sum_{n=0}^{\infty} \frac{(t-t_0)^n g^{(n)}(t_0)}{n!} .$$ Note that the $$g^{(n)}(t_0)$$ denotes the derivative evaluated at $$t_0$$, where $$g^{(0)}(t_0) = g(t_0)$$.