Polynomials involving the floor function
Number Theory
2008-02-03 v1
Abstract
Some identities are presented that generalize the formula x^3 = 3x floor(x floor(x)) - 3 floor(x) floor(x floor(x)) + floor(x)^3 + 3 frac(x) frac(x floor(x)) + frac(x)^3 to a representation of the product x_0x_1 ... x_{n-1}.
Cite
@article{arxiv.math/9504229,
title = {Polynomials involving the floor function},
author = {Inger Johanne Håland and Donald E. Knuth},
journal= {arXiv preprint arXiv:math/9504229},
year = {2008}
}