Is there a generalized solution to truncated exponential?

Asked Oct 25 '20 at 01:09

Active Oct 25 '20 at 01:32

Viewed 33 times

There's no closed form for the solution to all polynomials, but for certain classes it may be generalizable.

For a table of polynomials $$\begin{align*} 1 \\ 1+t \\ 1 + t + \frac{1}{2}t^2 \\ 1 + t + \frac{1}{2}t^2 + \frac{1}{6}t^3 \\ ... \end{align*}$$ and so on, is there any kind of generalization for the inverse structure or roots of the partial truncation of the exponential function?

edited Oct 25 '20 at 01:32

asked Oct 25 '20 at 01:09

JRRs

Are you looking for an expression like this $\sum_{k = 0}^{n}\tfrac{1}{k!}x^k$? – JimmyK4542 Oct 25 '20 at 01:19
Yep – JRRs Oct 25 '20 at 01:20
1

Does this answer your question? Roots of the incomplete gamma function – Robert Israel Oct 25 '20 at 01:57
One of the answers literally just gave up in the middle. So how do I know a closed form isn't possible versus someone saying "I personally don't know the answer" in which case their post isn't relevant? – JRRs Oct 25 '20 at 02:03

Is there a generalized solution to truncated exponential?

0 Answers0