Non-Commutative Q-Binomial Formula

2012/02/10 by Sengul Nalci, Oktay Pashaev, Nalci, Sengul +1
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Quantum Algebra (math.QA) #math.CO #math.QA

paper · pdf · doi:10.48550/arxiv.1202.2264

13 pages, 1 Figure

arxiv created 2012/02/10 · arxiv updated 2012/02/13

Abstract

In this paper, we found new q-binomial formula for Q-commutative operators. Expansion coefficients in this formula are given by q-binomial coefficients with two bases (q,Q), determined by Q-commutative q-Pascal triangle. Our formula generalizes all well-known binomial formulas in the form of Newton, Gauss, symmetrical, non-commutative and Binet-Fibonacci binomials. By our non-commutative q-binomial, we introduce q-analogue of function of two non-commutative variables, which could be used in study of non-commutative q-analytic functions and non- commutative q-traveling waves.

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