Том 71
№ 9

All Issues

Stanimirovic S.

Articles: 1
Brief Communications (English)

A matrix approach to the binomial theorem

Stanimirovic S.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2012. - 64, № 11. - pp. 1578-1584

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.