Another Power Identity Involving Binomial Theorem and Faulhaber's Formula
preprint
OA: closed
CC-BY-4.0
Abstract
In this paper, we derive and prove, by means of Binomial theorem and Faulhaber's formula, the following identity between $m$-order polynomials in $T$ $$\sum_{k=1}^{\ell}\sum_{j=0}^m A_{m,j}k^j(T-k)^j=\sum_{k=0}^{m}(-1)^{m-k}U_m(\ell,k)\cdot T^k=T^{2m+1}, \ \ell=T\in\mathbb{N}.$$
My notes (saved in your browser only)
Citation neighborhood (no data yet)
We don't have any in-corpus citations linked to this paper yet. The paper's references may be in our DB but unresolved to ``paper_id`` (resolution happens at ingest when the cited DOI matches a row we already have). Run the cross-source citation reconcile pass to retry.
Source provenance
- europepmc
- last seen: 2026-05-19T01:45:01.086888+00:00
- unpaywall
- last seen: 2026-05-28T02:00:01.590549+00:00
License: CC-BY-4.0