, Volume 14, Issue 4, pp 303-341

The calculus of finite differences over certain systems of numbers

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Abstract

A recursive process of interpolation over functions whose arguments belong to certain systems of numbers is described. The process can, in particular, be applied to functions of many variables and, for the examples considered, is both more flexible and more powerful than either the use of many dimensional divided differences or multivariate Lagrange interpolation. Recursive processes of differentiation, integration, and confluent interpolation over functions whose arguments belong to certain further systems of numbers are developed from the interpolation procedure.