Generalized Leibniz functional matrices and divided difference form of the Lagrange–Bürmann formula

In this paper, we derive two versions of divided difference form of the Lagrange–Bürmann expansion formula. The first version expresses all coefficients by a form of a determinant. By means of the factorizations of the generalized Leibniz functional matrices with respect to a sequence, we obtain the second version with coefficients represented by a finite sum. Some new matrix inversions are also investigated.