𝔖 Bobbio Scriptorium
✦   LIBER   ✦

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

✍ Scribed by D.A. Wolfram

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
176 KB
Volume
29
Category
Article
ISSN
0747-7171

No coin nor oath required. For personal study only.

✦ Synopsis

We give a formula for the general solution of a dth-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.

πŸ“œ SIMILAR VOLUMES

A Combinatorial Formula for the Lineariz
A Combinatorial Formula for the Linearization Coefficients of General Sheffer Polynomials
✍ Dongsu Kim; Jiang Zeng πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 341 KB

We prove a formula for the linearization coefficients of the general Sheffer polynomials, which unifies all the special known results for Hermite, Charlier, Laguerre, Meixner and Meixner-Pollaczek polynomials. Furthermore, we give a new and explicit real version of the corresponding formula for Meix