Booles formula as a consequence of Lagranges Interpolating Polynomial theorem

We present a slightly more general version of Boole’s additive formula for factorials as a simple consequence of Lagrange’s Interpolating Polynomial theorem.

💡 Research Summary

The paper revisits Boole’s additive formula, a classical identity that relates factorials to a finite alternating sum, and shows that a slightly more general version follows directly from the Lagrange interpolation theorem. The classical Boole identity is usually written as

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