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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