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Ukrainian Mathematical Journal

, Volume 64, Issue 11, pp 1784–1792 | Cite as

A matrix approach to the binomial theorem

  • S. Stanimirović
Article
  • 218 Downloads
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.

Keywords

Algebraic Property Matrix Approach Toeplitz Matrix Matrix Relation Fibonacci Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • S. Stanimirović
    • 1
  1. 1.University of NišNišSerbia

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