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  • 标题:The Optimal Estimation of the Turan-type Inequality for the Gamma Function and Its Numerical Method
  • 本地全文:下载
  • 作者:Zhongfeng Sun ; Huizeng Qin
  • 期刊名称:Engineering Letters
  • 印刷版ISSN:1816-093X
  • 电子版ISSN:1816-0948
  • 出版年度:2020
  • 卷号:28
  • 期号:4
  • 页码:1075-1080
  • 语种:English
  • 出版社:Newswood Ltd
  • 摘要:In this paper, we demonstrate that are strictly convex on (0,+∞) for all n = 1,3,..., and there exists a unique global minimum x n of ∆ n (x) for each odd positive integer n. On the other hand, we develop the algorithm for calculating the global minimum or the zero point of ∆ n (x) based on the Newton’s method and the recurrence relation of Γ (n) (x) associated with the Digamma function, the numerical results show that it’s more effective than other two algorithms. Furthermore, we find that ∆ n (x n ) is strictly increasing and ∆ n (x n ) ? α = 0.6359.
  • 关键词:Turán-type Inequality; Gamma Function; Digamma Function; Newton’s Method.
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