n阶变系数线性差分方程的解*
Solutions of the General n-th Order Variable Coefficients Linear Difference Equation
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摘要: 本文利用变数算符[2]以及给出变数算符和移动算符的乘积关系,并定义变系数移动算符幂级数间的乘积且证明其在Mikuiński收敛意义下是正确的；另外,把一般的n阶变系数线性差分方程转化为一个恰当的算符方程组,从而获得一般n阶变系数线性差分方程的解。
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关键词:
- Mikusiński算符 /
- 变系数线性差分方程 /
- 算符方程
Abstract: In this paper.variable operator and its product with shifting operator are studied.The product of power series of shifting operator with variable coefficient is defined andits convergence is proved under Mikusinski's sequence convergence.After turning ageneral variable coefficient linear difference equation of the n-th order wichi is turned into a set of operatorequations.we can obtain the solutions of the general n-theth order variable coefficientlinear difference equation.-
Key words:
- Mikusinskis operator /
- variable operator /
- convergence
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[1] Mikusi#324;ski.Oprotional Calculus,Pergaman Press,sth.ed.,New York(1959). [2] Qiu Lian-rong,A direct method of operational calculus(I).Acfa Mathematia Scientia.2(4)(1982).389-402. [3] 周之虎,关于《算符演算》中移动算符级数的一点注记,数学的实践与认识,(4)(1990),90-92. -
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