摘要
探讨了由非齐次线性递推关系gn+2=gn+1+gn+Atn,n≥0,A≠0且t≠0所定义的数列{gn}的一些基本性质;利用Elmore技巧和{gn}的指数生成函数推广了{gn},得到一个新的序列Gn(x),并证明了Gn(x)满足线性递推关系Gn+2=Gn+1+Gn+Atnext;最后,利用广义三角函数和新定义的序列{Qn(x)}再次扩展了序列{Gn(x)},给出并证明了它所满足的递推关系.
First, the basic properties of the sequence {gn} that was defined by a non-homogeneous linear recurrence rela- tiongn＋2=gn＋1＋gn＋Atn,n≥0,A≠0 were discussed; Secondly, the sequence {g} was generalized by using the techniques of Elmore and exponential generating function of {g}. Thus, we got a new sequence that satisfied a linear recurrence relation Gn＋2=Gn＋1＋Gn＋Atnext finally, the sequence {G.（x）} was generalized again by using generalized trigonometric functions and rede- fined sequence {Gn（x）}, in addition, its recurrence relation was given and proved.
出处
《海南师范大学学报（自然科学版）》
CAS
2015年第2期139-140,150,共3页
Journal of Hainan Normal University（Natural Science）
