The r-central factorial numbers with even indices
Abstract In this paper, we introduce the r-central factorial numbers with even indices of the first and second kind as extended versions of the central factorial numbers with even indices of both kinds. We obtain several fundamental properties and identities related to these numbers. The connections...
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SpringerOpen
2020-06-01
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| Series: | Advances in Difference Equations |
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| Online Access: | http://link.springer.com/article/10.1186/s13662-020-02763-1 |
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doaj-13c458f88aea44fc90d081552cda6bc92020-11-25T03:06:35ZengSpringerOpenAdvances in Difference Equations1687-18472020-06-012020111610.1186/s13662-020-02763-1The r-central factorial numbers with even indicesF. A. Shiha0Department of Mathematics, Faculty of Science, Mansoura UniversityAbstract In this paper, we introduce the r-central factorial numbers with even indices of the first and second kind as extended versions of the central factorial numbers with even indices of both kinds. We obtain several fundamental properties and identities related to these numbers. The connections between the new numbers and the Stirling numbers are presented. In addition, we give the probability distribution of the unsigned r-central factorial numbers with even indices. Finally, we consider the r-central factorial matrices and study some of their properties.http://link.springer.com/article/10.1186/s13662-020-02763-1r-central factorial numbers with even indicesPascal matrixStirling numbers |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
F. A. Shiha |
| spellingShingle |
F. A. Shiha The r-central factorial numbers with even indices Advances in Difference Equations r-central factorial numbers with even indices Pascal matrix Stirling numbers |
| author_facet |
F. A. Shiha |
| author_sort |
F. A. Shiha |
| title |
The r-central factorial numbers with even indices |
| title_short |
The r-central factorial numbers with even indices |
| title_full |
The r-central factorial numbers with even indices |
| title_fullStr |
The r-central factorial numbers with even indices |
| title_full_unstemmed |
The r-central factorial numbers with even indices |
| title_sort |
r-central factorial numbers with even indices |
| publisher |
SpringerOpen |
| series |
Advances in Difference Equations |
| issn |
1687-1847 |
| publishDate |
2020-06-01 |
| description |
Abstract In this paper, we introduce the r-central factorial numbers with even indices of the first and second kind as extended versions of the central factorial numbers with even indices of both kinds. We obtain several fundamental properties and identities related to these numbers. The connections between the new numbers and the Stirling numbers are presented. In addition, we give the probability distribution of the unsigned r-central factorial numbers with even indices. Finally, we consider the r-central factorial matrices and study some of their properties. |
| topic |
r-central factorial numbers with even indices Pascal matrix Stirling numbers |
| url |
http://link.springer.com/article/10.1186/s13662-020-02763-1 |
| work_keys_str_mv |
AT fashiha thercentralfactorialnumberswithevenindices AT fashiha rcentralfactorialnumberswithevenindices |
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