乘积型常系数递推关系的相关性质  

On the Product Type Recurrence Relations with Constant Coefficients

作　　者：张上伟[1] 吴康[1] 

机构地区：[1]华南师范大学数学科学学院,广东广州510631

出　　处：《汕头大学学报（自然科学版）》2013年第4期28-33,共6页Journal of Shantou University：Natural Science Edition

摘　　要：定义乘积型常系数非齐次递推关系、乘积型常系数(非)齐次递推关系组,研究其相关性质及数列通项公式的求法.分别在{A1,n},{A2,n},…,{Ak,n}是正实数列,p1,p2,…,p k是实数以及{A1,n},{A2,n},…,{Ak,n}是复数列,p1,p2,…,p k是整数这两种情况下研究乘积型常系数(非)齐次递推关系组的相关性质,得到相应的性质和定理.In this research, the Product Type Non-homogeneous Recurrence Relations with Constant Coefficients, the combination of the Product Type Homogeneous Recurrence Relations with Constant Coefficients and the combination of the Product Type Non-homogeneous Recurrence Relations with Constant Coefficients are defined. Also, the related characterization and the general term formula are investigated under two circumstances,one of which is when {A1,n},{A2,n},…,{Ak,n} are sequences of positive real numbers,p1,p2,…,pk are real numbers,the other is when {A 1,n},{A 2,n},…,{A k,n}are complex sequences,p1,p2,…,pk are integers. The related characterizations of the combination of the Product Type Homogeneous Recurrence Relations with Constant Coefficients are discussed and some related characterization are also generated.

关 键 词：乘积型常系数非齐次递推关系 递推关系组 通项公式 

分 类 号：O151.1[理学—数学]