MHB What is the correct power series for $g(t)$?

[Dustinsfl]

What would be the power series of $g(t)$?

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

This?

 

[tkhunny]

?? What EXACTLY are you trying to do? I'm guessing the recursive definition you have suggested is not a good way to go.

 

[CaptainBlack]

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 \( g^{(0)}(t_0) = g(t_0) \).

Does this help you?

Edit: Sorry, to be specific this is the Taylor power series.

 

[Dustinsfl]

There was a mistake in what I was reading, i.e. is read it wrong. I see what my issue was so the question I asked was wrong.