Solutions of the generaln-th order variable coefficients linear difference equation
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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 wordsMikusiński’s operator variable operator convergence linear difference equation with variable coeffcients solution of series form operator equation
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