Exact Discrete Analogs of Derivatives of Integer Orders: Differences as Infinite Series
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 demo...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2015-01-01
|
| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2015/134842 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832563010905833472 |
|---|---|
| author | Vasily E. Tarasov |
| author_facet | Vasily E. Tarasov |
| author_sort | Vasily E. Tarasov |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-5319d6723fb540b6a111f16fc9b5d36b |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-5319d6723fb540b6a111f16fc9b5d36b2025-02-03T01:21:10ZengWileyJournal of Mathematics2314-46292314-47852015-01-01201510.1155/2015/134842134842Exact Discrete Analogs of Derivatives of Integer Orders: Differences as Infinite SeriesVasily E. Tarasov0Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 119991, RussiaNew 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.http://dx.doi.org/10.1155/2015/134842 |
| spellingShingle | Vasily E. Tarasov Exact Discrete Analogs of Derivatives of Integer Orders: Differences as Infinite Series Journal of Mathematics |
| title | Exact Discrete Analogs of Derivatives of Integer Orders: Differences as Infinite Series |
| title_full | Exact Discrete Analogs of Derivatives of Integer Orders: Differences as Infinite Series |
| title_fullStr | Exact Discrete Analogs of Derivatives of Integer Orders: Differences as Infinite Series |
| title_full_unstemmed | Exact Discrete Analogs of Derivatives of Integer Orders: Differences as Infinite Series |
| title_short | Exact Discrete Analogs of Derivatives of Integer Orders: Differences as Infinite Series |
| title_sort | exact discrete analogs of derivatives of integer orders differences as infinite series |
| url | http://dx.doi.org/10.1155/2015/134842 |
| work_keys_str_mv | AT vasilyetarasov exactdiscreteanalogsofderivativesofintegerordersdifferencesasinfiniteseries |