Polynomials involving the floor function
Inger Johanne Håland, Donald E. Knuth
Abstract
Some identities are presented that generalize the formula x3 = 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 x0x1 ... xn-1.
Create a lesson
Related papers
An Infinite Family of Apéry-like Recurrences for Euler's Constant
Rotem Kalisch, Tali Monderer, Elyasheev Leibtag et al.
On the saturability of p-adic Lie groups
Casey Perdue
On Divisor Function Polynomials and Dirichlet Series
Martin N. Huxley, Matthew C. Lettington, Karl Michael Schmidt
On a conjecture on Romanoff type representations
Xiao-Hui Yan
Regularization of a Divergent Arithmetic Product via the Asymptotic Monoid: The Case of (-1)ω(n)
A. Alvarez Cruz, E. A. Alvarez Gutierrez
Appell Sequences in Analytic Number Theory: Shifted Expansions and Dirichlet L-Functions
Abdelmejid Bayad