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In this paper, we derive and prove, by means of Binomial theorem and Faulhaber's formula, the following identity between $m$-order polynomials in \(T\) \(\sum_{k=1}^{\ell}\sum_{j=0}^m A_{m,j}k^j(T-k)^j=\sum_{k=0}^{m}(-1)^{m-k}U_m(\ell,k)\cdot T^k=T^{2m+1}, \ \ell=T\in\mathbb{N}.\)
The main aim of this paper to establish the relations between forward, backward and central finite (divided) differences (that is discrete analog of the derivative) and partial & ordinary high-order derivatives of the polynomials.
Cour 1 ere AS
Primality Tests and Factoring Algorithms
Two Snow Plows Problem
"(Infinite) series are the invention of the devil, by using them, on may draw any conclusion he pleases, and that is why these series have produced so many fallacies and so many paradoxes." -Neils Hendrik Abel
Señales y Sistemas
Fortgeschrittenenpraktikum Astronomie Hausarbeit an der Universitäts-Sternwarte München (LMU).
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