Applied Mathematics and Mechanics

, Volume 15, Issue 3, pp 235–246 | Cite as

Solutions of the generaln-th order variable coefficients linear difference equation

  • Zhou Zhi-hu


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 and its convergence is proved under Mikusiński’s sequence convergence. After turning a general variable coefficient linear difference equation of order n into a set of operator equations, we can obtain the solutions of the general n-th order variable coefficient linear difference equation.

Key words

Mikusiński’s operator variable operator convergence linear difference equation with variable coeffcients solution of series form operator equation 


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  1. [1]
    Mikusiński, J.,Operational Calculus, Pergamon Press, 5th ed., New York (1959).Google Scholar
  2. [2]
    Qiu Lian-rong, A direct method of operational calculus [I],Acts Math. Scientia,2, 4 (1982), 389–402.MATHGoogle Scholar
  3. [3]
    Zhou Zhi-hu, A note on the series of shifting operator in “Operational Calculus”,Math. in Practice and Theory, 4, (1990), 90–92. (in Chinese)Google Scholar

Copyright information

© SUT 1994

Authors and Affiliations

  • Zhou Zhi-hu
    • 1
  1. 1.Anhui Architecture Industry CollegeHefei

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