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 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.
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References
Mikusiński, J.,Operational Calculus, Pergamon Press, 5th ed., New York (1959).
Qiu Lian-rong, A direct method of operational calculus [I],Acts Math. Scientia,2, 4 (1982), 389–402.
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)
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Communicated by Lin Zong-chi
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Zhi-hu, Z. Solutions of the generaln-th order variable coefficients linear difference equation. Appl Math Mech 15, 235–246 (1994). https://doi.org/10.1007/BF02451059
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DOI: https://doi.org/10.1007/BF02451059