一些组合三角的生成递推式  

THE GENERATING RECURSION FORMULA OF SOME COMBINATORIAL TRIANGLE

作　　者：党四善[1] 

机构地区：[1]西北轻工业学院基础课部

出　　处：《西北轻工业学院学报》1991年第4期77-82,112,共6页Journal of Northwest University of Light Industry

摘　　要：本文通过对递推式 R(λ,μ)=R(λ-1,μ)+R(λ,μ-1)的研究重新得到杨辉三角、双进组合三角;发现了又一种新的组合三角——非对称双进组合三角;利用非对称双进组合三角,简化了不定积分dx/sln^mxcos^nx(m,n 是奇正整数)的计算并初等地推导出二项式级数1,2,……)。In this paper,Pascal-Triangle and combinatorial triangle with repetition are regained through the study of recursion R(λ,μ)=R(λ-1,μ)+R(λ,μ-1); a new combinatorial triangle(asymmetrcial combinatorial triangle with repeti- tion)is discovered.Usirg asymmetrical(combinat triange with repetiter, the computation of indefinite integraldx/sin^mxcos^nx (here,m,n is odd positive integer)is simplified and the binamial series (1-x)^(-n+1)=sum from r=9 to t∞ C^x_n+_rX^r(|x|<1,n=0,1,2,…) is elementarily derived.

关 键 词：组合三角 生成递推式 非对称双进组合三角 

分 类 号：O157.3[理学—数学]