difference equation

difference equation (plural difference equations)

1. (mathematics) An equation involving an ordered sequence of real numbers (${\displaystyle \left\{a_{n}\right\}_{n=1}^{\infty }}$ ) and some of its differences, where the first difference is defined as ${\displaystyle \Delta (a_{n})=a_{n+1}-a_{n}\,}$ and the k^th difference is defined recursively as ${\displaystyle \Delta ^{k}(a_{n})=\Delta ^{k-1}(a_{n+1})-\Delta ^{k-1}(a_{n})\,}$ .
2. (mathematics) more broadly, any recurrence relation

• differential equation