Difference equations : Linear difference equations with non-constant coefficients

Linear difference equations with non-constant coefficients
Difference equations

Authors : Guoting CHEN, Jean DELLA DORA

Publication date: October 10, 2007 | Lire en français

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3. Linear difference equations with non-constant coefficients

These are equations associated with an operator L = a ₀ τ^r + ... + a_r, but, now, the a_i are functions of n. Therefore, for any integer n :

a_{0} (n) f (r + n) + \dots + a_{r} (n) f (n) = g (n)

for a non-homogeneous equation.

Let's consider the case of homogeneous equations.

How can we follow the same approach as for equations with constant coefficients?

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Linear difference equations with non-constant coefficients

(1) - ABRAMOV (S.A.), PETKOVSEK (M.) - D'Alembertian solutions of nonhomogeneous linear ordinary differential and difference equations. - Manuscrit (1994).
(2) - ADAMS (C.R.) - On the irregular cases of linear ordinary difference equations. - Trans. Amer. Math. Soc., 30, 507-541 (1928).

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