 |
 |
Algebra |
|
Authors: Habeeb Mohammed
We investigate how the sequence $f^{(n)}(0)$ acts for a specific class of functions: exponentiated polynomials, $e^{p(x)}$, of which we first look at $e{-x^2}$. This leads us into an textit{infinite dimensional matrix}, which can be analysed via tools from Lie algebra. To generalise this to all polynomials $p(x)$, we define a correspondence between the space of derivatives of $e^{p(x)}$, $cal{F}$, and a general vector space of polynomials, $cal{T}$; we find that the derivative in $cal{F}$ also corresponds to an operator in $cal{T}$. We then utilise Zassenhaus' formula to find how this operator iterates, hence giving us a general formula for the $n$th derivative of $e^{p(x)}$.
Comments: 14 Pages.
Download: PDF
[v1] 2026-02-21 21:53:57
Unique-IP document downloads: 83 times
Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.
Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.
| Third-Party Links: |
|