difference equation

Noun

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