abstract | reasoning

Author: kolosovpetro

CHANGELOG.md

@@ -10,6 +10,7 @@ and this project adheres to [Semantic Versioning v2.0.0](https://semver.org/spec
 ### Changed
 
 - Improve reasoning
+- Update abstract
 
 ## [1.0.3] - 2025-02-24
 

out/AnEfficientMethodOfSplineApproximation.pdf

@@ -1,6 +1,6 @@
 Let $P(m, X, N)$ be an $m$-degree polynomial in $X\in\mathbb{R}$
 having fixed non-negative integers $m$ and $N$.
-Essentially, the polynomial $P(m, X, N)$ is a result of a rearrangement inside Faulhaber's formula
+The polynomial $P(m, X, N)$ is derived from a rearrangement of Faulhaber's formula
 in the context of Knuth's work entitled "Johann Faulhaber and sums of powers".
 In this manuscript we discuss the approximation properties of polynomial $P(m,X,N)$.
 In particular, the polynomial $P(m,X,N)$ approximates the odd power function $X^{2m+1}$ in a certain neighborhood

src/sections/01_abstract.tex

@@ -16,7 +16,7 @@
 For example,
 \input{sections/figures/05_fig_coefficients_a}
 
-Essentially, the polynomial $P(m, X, N)$ is derived from a rearrangement of Faulhaber's formula
+The polynomial $P(m, X, N)$ is derived from a rearrangement of Faulhaber's formula
 in the context of Knuth's work entitled \textit{Johann Faulhaber and sums of powers}, see~\cite{knuth1993johann}.
 In particular, the polynomial $P(m, X, N)$ yields an identity for odd powers
 \begin{align*}