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[SOLVED] power series

dwsmith

Well-known member
Feb 1, 2012
1,673
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
Jan 27, 2012
267
?? 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
Jan 26, 2012
890
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

"Read Euler, read Euler." - Laplace
MHB Math Helper
Feb 29, 2012
342
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.
 

dwsmith

Well-known member
Feb 1, 2012
1,673
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.