A matrix approach to the binomial theorem

• Дата: 2012
• Автори: Stanimirovic, S., Станіміровіч, С.
• Формат: Стаття
• Мова: Англійська
• Опубліковано: Institute of Mathematics, NAS of Ukraine 2012
• Онлайн доступ: https://umj.imath.kiev.ua/index.php/umj/article/view/2684
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

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...