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Polynomials involving the floor function

Inger Johanne Håland·Donald E. Knuth
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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}.

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Inger Johanne Håland, Donald E. Knuth. 1995-04-01. Polynomials involving the floor function. https://arxiv.org/abs/math/9504229

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