Motivated by the formula
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 the generalization of the binomial theorem is introduced. Numerous combinatorial identities are obtained from these matrix relations.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 11, pp. 1578–1584, November, 2012.
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Stanimirović, S. A matrix approach to the binomial theorem. Ukr Math J 64, 1784–1792 (2013). https://doi.org/10.1007/s11253-013-0752-3
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DOI: https://doi.org/10.1007/s11253-013-0752-3