readme

Author: kolosovpetro

README.md

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 # An efficient method of spline approximation for power function
+
+Let $P(m, X, N)$ be an $m$-degree polynomials in $X\in\mathbb{R}$
+having fixed non-negative integers $m$ and $N$.
+Essentially, the polynomial $P(m, X, N)$ is a result of rearrangement inside Faulhaber's formula
+in context of Knuth's work Johann Faulhaber and sums of powers.
+
+In this manuscript we discuss approximation properties of polynomial $P(m,X,N)$.
+In particular, the polynomial $P(m,X,N)$ approximates odd power function $X^{2m+1}$ in certain neighborhood
+of fixed non-negative integer $N$ with percentage error lesser than $1\%$.
+
+By increasing the value of $N$ the length of convergence interval with odd-power $X^{2m+1}$ increasing as well.
+
+Furthermore, this approximation technique is generalized for arbitrary non-negative exponent power function $X^j$
+by using splines.