Boole's formula as a consequence of Lagrange's Interpolating Polynomial theorem

TL;DR

This paper derives Boole's factorial formula as a direct consequence of Lagrange's Interpolating Polynomial theorem, providing a more general perspective on the relationship between factorials and polynomial interpolation.

Contribution

It introduces a generalized version of Boole's formula derived from Lagrange's Interpolating Polynomial theorem, linking factorials to polynomial interpolation.

Findings

Boole's formula can be derived from Lagrange's Interpolating Polynomial theorem.

A more general version of Boole's factorial formula is presented.

The connection between factorials and polynomial interpolation is clarified.

Abstract

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