Number Theory

    

Inversion Identity for The $k$-th Root Function

Authors: Niccan Mandal

In this paper, we derive a formal inversion identity from the Taylor expansion of $sqrt[k]{x}$ to get $x$ as an infinite series of the function. Along with the derivation, we also give a proof of the identity by justifying some crucial mathematically rigorous statements regarding analyticity, validity of Cauchy's convolution, and the convergence, and also derive a trivial infinite series for $pi$, $e$ (Euler's constant) and a formal infinite series identity of $gamma$ (Euler-Mascheroni constant) in terms of their $k$-th roots.

Comments: 8 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

Download: PDF

Submission history

[v1] 2026-02-24 21:55:54

Unique-IP document downloads: 118 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.

comments powered by Disqus