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A matrix approach to the binomial theorem

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Ukrainian Mathematical Journal Aims and scope

Motivated by the formula

$$ {x^n}=\sum\limits_{k=0}^n {\left( {\begin{array}{*{20}{c}} n \\ k \\ \end{array}} \right){{{\left( {x-1} \right)}}^k},} $$

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 the generalization of the binomial theorem is introduced. Numerous combinatorial identities are obtained from these matrix relations.

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Authors and Affiliations

  1. University of Niš, Niš, Serbia

    S. Stanimirović

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  1. S. Stanimirović
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Additional information

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

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