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

Vasily E. Tarasov
2015 Journal of Mathematics  
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 ordersnare 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.
doi:10.1155/2015/134842 fatcat:vzs74nkwmbhy5ojyq5no3qnfd4