Start with the Taylor expansion of about a point :

Jets may also be seen as the coordinate free versions of Taylor expansions.

Another possibility is to consider the Taylor expansion of the function around :

Essentially, by using a Taylor expansion you can derive a closed form relationship between these two representations.

It can be considered a Taylor expansion of at .

If a truncated Taylor expansion of is performed, this would be missed.

Therefore we can extend the limits of integration beyond the limit for a Taylor expansion.

The expression above may be viewed as a Taylor expansion of the full quantum dimension.

The value of can be approximated using the Taylor expansion.

However, this is only an approximation due to the terms that were ignored from the Taylor expansion.