On a Difference Matrix and Its Properties (Analysis in Theory and Applications, 2017)
In the present paper, a new difference matrix via difference operator $D$ isintroduced. Let $x = (x_k)$ be a sequence of real numbers, then the difference operator $D$ is defined by $D(x)_n = ∑^n_{k=0} (−1)^k\Bigg(\begin{matrix}n \\ n−k \end{matrix}\Bigg)x_k$, where $n = 0,1,2,3,···$. Several interestingproperties of the new operator $D$ are discussed.