Non-Commutative Q-Binomial Formula
Quantum Algebra
2012-02-13 v1 Combinatorics
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.
Cite
@article{arxiv.1202.2264,
title = {Non-Commutative Q-Binomial Formula},
author = {Sengul Nalci and Oktay Pashaev},
journal= {arXiv preprint arXiv:1202.2264},
year = {2012}
}
Comments
13 pages, 1 Figure