| Tianxiao HE.A Unified Approach to Generalized Stirling Functions[J].数学研究及应用,2012,32(6):631~640 |
| A Unified Approach to Generalized Stirling Functions |
| A Unified Approach to Generalized Stirling Functions |
| 投稿时间：2012-02-03 修订日期：2012-05-22 |
| DOI：10.3770/j.issn:2095-2651.2012.06.001 |
| 中文关键词: Stirling numbers Stirling functions factorial polynomials generalized factorial divided difference $k$-Gamma functions Pochhammer symbol and $k$-Pochhammer symbol. |
| 英文关键词:Stirling numbers Stirling functions factorial polynomials generalized factorial divided difference $k$-Gamma functions Pochhammer symbol and $k$-Pochhammer symbol. |
| 基金项目: |
|
| 摘要点击次数: 3783 |
| 全文下载次数: 3967 |
| 中文摘要: |
| Here presented is a unified approach to generalized Stirling functions by using generalized factorial functions, $k$-Gamma functions, generalized divided difference, and the unified expression of Stirling numbers defined in [16]. Previous well-known Stirling functions introduced by Butzer and Hauss [4], Butzer, Kilbas, and Trujilloet [6] and others are included as particular cases of our generalization. Some basic properties related to our general pattern such as their recursive relations, generating functions, and asymptotic properties are discussed, which extend the corresponding results about the Stirling numbers shown in [21] to the defined Stirling functions. |
| 英文摘要: |
| Here presented is a unified approach to generalized Stirling functions by using generalized factorial functions, $k$-Gamma functions, generalized divided difference, and the unified expression of Stirling numbers defined in [16]. Previous well-known Stirling functions introduced by Butzer and Hauss [4], Butzer, Kilbas, and Trujilloet [6] and others are included as particular cases of our generalization. Some basic properties related to our general pattern such as their recursive relations, generating functions, and asymptotic properties are discussed, which extend the corresponding results about the Stirling numbers shown in [21] to the defined Stirling functions. |
| 查看全文 查看/发表评论 下载PDF阅读器 |
|
|
|
