A functional equation arising from multiplication of quantum integers

[摘要] For the quantum integer [n](q) = 1 + q + q(2) + ... + q(n-1) there is a natural polynomial multiplication such that This multiplication leads to the functional equation [m](q) circle times (q)[n](q) = [mn](q). defined on a given sequence f(m)(q)f(n)(q(m)) = f(mn)(q), defined on a given sequence F = {f(n)(q)}(n=1)(infinity) of polynomials. This paper contains various results concerning the construction and classification of polynomial sequences that satisfy the functional equation, as well open problems that arise from the functional equation. (C) 2003 Elsevier Inc. All rights reserved.

[发布日期] 2003-12-01

[关键词] quantum integers;quantum polynomial;polynomial functional equation;q-series;additive bases