# A Formula for the General Solution of a Constant-coefficient Difference Equation

## Date

2000

## Authors

Wolfram, David

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## Publisher

Academic Press

## Abstract

We give a formula for the general solution of a d th-order linear difference equation with constant coefficients in terms of one of the solutions of its associated homogeneous equation. The formula neither uses the roots of the characteristic equation nor their multiplicities. It can be readily generalized to the case where the domain of the difference equation is the real numbers, and the initial values are given by a function defined on the interval [0,d ). In both cases, we express the general solution of the difference equation in terms of a single solution of its associated homogeneous equation at integer arguments.

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## Source

Journal of Symbolic Computation

## Type

Journal article

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## DOI

10.1006/jsco.1999.0350

## Restricted until

2037-12-31