2017
Том 69
№ 9

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A matrix approach to the binomial theorem

Stanimirovic S.

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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.

English version (Springer): Ukrainian Mathematical Journal 64 (2012), no. 11, pp 1784-1792.

Citation Example: Stanimirovic S. A matrix approach to the binomial theorem // Ukr. Mat. Zh. - 2012. - 64, № 11. - pp. 1578-1584.

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