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A Leibniz formula for multivariate divided differences
"... The Leibniz formula, for the divided difference of a product, and Opitz’s formula, for the divided difference table of a function as the result of evaluating that function at a certain matrix, are shown to be special cases of a formula available for the coefficients, with respect to any basis, of an ..."
Abstract

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The Leibniz formula, for the divided difference of a product, and Opitz’s formula, for the divided difference table of a function as the result of evaluating that function at a certain matrix, are shown to be special cases of a formula available for the coefficients, with respect to any basis, of an ‘ideal’ or ‘Hermite’ polynomial interpolant, in any number of variables.