difference equation

English

Noun

difference equation (plural difference equations)

Examples (restricted sense)
$3{\mathrm{\Delta }}^2(a_n)+2\mathrm{\Delta }(a_n)+7a_n=0$

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

Translations

math: type of equation

• Finnish: differenssiyhtälö

recurrence relation — see recurrence relation

See also

• differential equation