# Difference between Taylor Series Expansion and Taylor Series

Is there a difference in the meaning of Taylor Series and Taylor Series Expansion? For example:

The Taylor Series of the exponential function about $$0$$ is: $$e^x = \sum_{n=0}^{\infty}\frac{x^n}{n!}$$

Whereas the Taylor Series Expansion about $$0$$ is: $$e^x = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + ...$$

Is this correct? I don't mean to be overly pedantic, but I am interested in knowing if there is actually a difference in their definitions. Thank you!

• Difference between what and what? In fact $\sum\frac{x^n}{x!}$ and $1+x+\dots$ are exactly the same expansion, in different notation. So you asking about the difference between something and itself. Commented Apr 30, 2020 at 13:15
• I am asking if there is a difference. Perhaps Taylor Series is strictly reserved for the summation notation where as Taylor Series Expansion is reserved for the "expanded" notation. I know that both are equal to $e^x$, I was just wondering about the wording. Commented Apr 30, 2020 at 14:13
• "I am asking if there is a difference." I understood that - that's why I explained that there is no difference. There is no difference between $4$ and $2+2$; they're exactly the same thing Commented Apr 30, 2020 at 22:23