A Newton Interpolation Approach to Generalized Stirling Numbers
We employ the generalized factorials to define a Stirling-type pair {s(n,k;α,β,r),S(n,k;α,β,r)} which unifies various Stirling-type numbers investigated by previous authors. We make use of the Newton interpolation and divided differences to obtain some basic properties of the generalized Stirling nu...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/351935 |
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| author | Aimin Xu |
| author_facet | Aimin Xu |
| author_sort | Aimin Xu |
| collection | DOAJ |
| description | We employ the generalized factorials to define a Stirling-type pair {s(n,k;α,β,r),S(n,k;α,β,r)} which unifies various Stirling-type numbers investigated by previous authors. We make use of the Newton interpolation and divided
differences to obtain some basic properties of the generalized Stirling numbers including the recurrence relation, explicit expression, and generating function. The generalizations of the well-known Dobinski's formula are further investigated. |
| format | Article |
| id | doaj-art-cbd13d77dfb24ed2a7816c8b774654cc |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-cbd13d77dfb24ed2a7816c8b774654cc2025-02-03T01:12:24ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/351935351935A Newton Interpolation Approach to Generalized Stirling NumbersAimin Xu0Institute of Mathematics, Zhejiang Wanli University, Ningbo 315100, ChinaWe employ the generalized factorials to define a Stirling-type pair {s(n,k;α,β,r),S(n,k;α,β,r)} which unifies various Stirling-type numbers investigated by previous authors. We make use of the Newton interpolation and divided differences to obtain some basic properties of the generalized Stirling numbers including the recurrence relation, explicit expression, and generating function. The generalizations of the well-known Dobinski's formula are further investigated.http://dx.doi.org/10.1155/2012/351935 |
| spellingShingle | Aimin Xu A Newton Interpolation Approach to Generalized Stirling Numbers Journal of Applied Mathematics |
| title | A Newton Interpolation Approach to Generalized Stirling Numbers |
| title_full | A Newton Interpolation Approach to Generalized Stirling Numbers |
| title_fullStr | A Newton Interpolation Approach to Generalized Stirling Numbers |
| title_full_unstemmed | A Newton Interpolation Approach to Generalized Stirling Numbers |
| title_short | A Newton Interpolation Approach to Generalized Stirling Numbers |
| title_sort | newton interpolation approach to generalized stirling numbers |
| url | http://dx.doi.org/10.1155/2012/351935 |
| work_keys_str_mv | AT aiminxu anewtoninterpolationapproachtogeneralizedstirlingnumbers AT aiminxu newtoninterpolationapproachtogeneralizedstirlingnumbers |