Exact Discrete Analogs of Derivatives of Integer Orders: Differences as Infinite Series

Abstract EN

New differences of integer orders, which are connected with derivatives of integer orders not approximately, are proposed.

These differences are represented by infinite series.

A characteristic property of the suggested differences is that its Fourier series transforms have a power-law form.

We demonstrate that the proposed differences of integer orders n are directly connected with the derivatives ∂n/∂xn.

In contrast to the usual finite differences of integer orders, the suggested differences give the usual derivatives without approximation.