A matrix approach to the binomial theorem

  • S. Stanimirovic Univ. Nis, Serbia

Abstract

Motivated by the formula $x^n = \sum_{k=0}^n\left(n \atop k\right) (x - 1)^k$ we investigate factorizations of the lower triangular Toeplitz matrix with $(i, j)$th entry equal to $x^{i-j}$ via the Pascal matrix. In this way, a new computational approach to a generalization of the binomial theorem is introduced. Numerous combinatorial identities are obtained from these matrix relations.
Published
25.11.2012
How to Cite
StanimirovicS. “A Matrix Approach to the Binomial Theorem”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, no. 11, Nov. 2012, pp. 1578-84, http://umj.imath.kiev.ua/index.php/umj/article/view/2684.
Section
Short communications