TY - JOUR
T1 - On a Difference Matrix and Its Properties
JO - Analysis in Theory and Applications
VL - 4
SP - 375
EP - 383
PY - 2017
DA - 2017/11
SN - 33
DO - http://doi.org/10.4208/ata.2017.v33.n4.7
UR - https://global-sci.org/intro/article_detail/ata/10704.html
KW - Difference operators $∆^α$, $B(r,s)$, $B(r,s,t,u)$, $D$, Cesàro operator $C(1,1)$.
AB - <p style="text-align: justify;">In the present paper, a new difference matrix via difference operator $D$ is
introduced. 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 interesting
properties of the new operator $D$ are discussed.</p>