Noun
(mathematics) An equation involving an ordered sequence of real numbers (
{
a
n
}
n
=
1
∞
{\displaystyle \left\{a_{n}\right\}_{n=1}^{\infty }}
) and some of its differences, where the first difference is defined as
Δ
(
a
n
)
=
a
n
+
1
−
a
n
{\displaystyle \Delta (a_{n})=a_{n+1}-a_{n}\,}
and the k difference is defined recursively as
Δ
k
(
a
n
)
=
Δ
k
−
1
(
a
n
+
1
)
−
Δ
k
−
1
(
a
n
)
{\displaystyle \Delta ^{k}(a_{n})=\Delta ^{k-1}(a_{n+1})-\Delta ^{k-1}(a_{n})\,}
.
(mathematics) more broadly, any recurrence relation
Source: en.wiktionary.orgThis results in : The difference equation (using the Direct Form I ) is : Frequency warping To determine the frequency response of a continuous-time filter, the transfer function is evaluated at which is on the axis. Source: Internet
For example, given a difference equation, one would set and for and evaluate. Source: Internet
In 1800, less than two years after his entry, he published two memoirs, one on Étienne Bézout 's method of elimination, the other on the number of integrals of a finite difference equation. Source: Internet
This nonlinear difference equation is intended to capture two effects: * reproduction where the population will increase at a rate proportional to the current population when the population size is small. Source: Internet