On factorization of q-difference equation for continuous q-Hermite polynomials
经典分析与常微分方程
2009-11-11 v2 量子代数
摘要
We argue that a customary q-difference equation for the continuous q-Hermite polynomials H_n(x|q) can be written in the factorized form as (D_q^2 - 1)H_n(x|q)=(q^{-n}-1)H_n(x|q), where D_q is some explicitly known q-difference operator. This means that the polynomials H_n(x|q) are in fact governed by the q-difference equation D_qH_n(x|q)=q^{-n/2}H_n(x|q), which is simpler than the conventional one.
引用
@article{arxiv.math/0602375,
title = {On factorization of q-difference equation for continuous q-Hermite polynomials},
author = {M. N. Atakishiyev and A. U. Klimyk},
journal= {arXiv preprint arXiv:math/0602375},
year = {2009}
}
备注
7 pages