Non-Commutative Q-Binomial Formula

Details Non-Commutative Q-Binomial Formula Non-Commutative Q-Binomial Formula

2012-02-10

arxiv.org/abs/1202.2264v1

Mathematics

Quantum Algebra

13 pages, 1 Figure

Scientific paper

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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