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.
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