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

Vasily E. Tarasov

Journal of Mathematics, 2015, vol. 2015, 1-8

Abstract:

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

Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:134842

DOI: 10.1155/2015/134842

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