The Bessel Numbers and Bessel Matrices  

作　　者：Sheng Liang YANG Zhan Ke QIAO 

机构地区：[1]Department of Applied Mathematics, Lanzhou University of Technoiogy, Gansu 730050, P. R. China [2]Department of Mathematics, Suzhou University of Science and Technology, Jiangsu 215009, P. R. China

出　　处：《Journal of Mathematical Research and Exposition》2011年第4期627-636,共10页数学研究与评论（英文版）

基　　金：Supported by the Natural Science Foundation of Gansu Province (Grant No.1010RJZA049)

摘　　要：In this paper, using exponential Riordan arrays, we investigate the Bessel numbers and Bessel matrices. By exploring links between the Bessel matrices, the Stirling matrices and the degenerate Stirling matrices, we show that the Bessel numbers are special case of the degenerate Stirling numbers, and derive explicit formulas for the Bessel numbers in terms of the Stirling numbers and binomial coefficients.In this paper, using exponential Riordan arrays, we investigate the Bessel numbers and Bessel matrices. By exploring links between the Bessel matrices, the Stirling matrices and the degenerate Stirling matrices, we show that the Bessel numbers are special case of the degenerate Stirling numbers, and derive explicit formulas for the Bessel numbers in terms of the Stirling numbers and binomial coefficients.

关 键 词：Bessel number of the first kind Bessel number of the second kind exponential Riordan array Stifling numbers Bessel matrix. 

分 类 号：O157.1[理学—数学]