A divided difference identity for a class of multiple integrals
This work addresses a theoretical problem in mathematics, specifically in integral calculus and polynomial theory, and appears incremental as it builds on known concepts like Vandermonde polynomials and divided differences.
The authors derived an identity connecting multiple integrals with Vandermonde polynomials to divided differences, providing an integral formula for divided differences, and showed that sums of pure and mixed partial derivatives of these polynomials are zero.
We derive an identity that relates a class of multiple integrals involving Vandermonde polynomials to divided differences. Alternatively the identity can be viewed as an integral formula for divided differences. As part of the derivation we show that both sums of pure partial derivatives and mixed partial derivatives of Vandermonde polynomials are zero, which might be of independent interest.