Lexic.us

Definition of Difference equation

1. Noun. (mathematics) An equation involving an ordered sequence or real numbers ($\backslash left\backslash \{a\_n\backslash right\backslash \}\_\{n=1\}^\backslash infty$) and some number if it's 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 $\backslash Delta^k(a\_n)\; =\; \backslash Delta^\{k-1\}(a\_\{n+1\})\; -\; \backslash Delta^\{k-1\}(a\_n)\backslash ,$. ¹

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