Recurrence relation
recurrence formula
A relation of the form
 |
permitting one to compute all members of the sequence 
if its first 
members are given. Examples of recurrence relations are: 1) 
, a geometric progression; 2) 
, an arithmetic progression; 3) 
, the sequence of Fibonacci numbers.
In the case where the recurrence relation is linear (see Recursive sequence) the problem of describing the set of all sequences that satisfy a given recurrence relation has an analogy with solving an ordinary homogeneous linear differential equation with constant coefficients.
References
| [1] | A.I. Markushevich, "Rekursive Folgen" , Deutsch. Verlag Wissenschaft. (1973) (Translated from Russian) |
Comments
A sequence of elements 
of a commutative ring 
with a unit element satisfies a linear recurrence relation 
, 
, if and only if the formal power series 
is a rational function of the form 
, with 
and 
a polynomial of degree 
.
Recurrence relation. S.N. Artemov (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Recurrence_relation&oldid=15946