recurrence relation

Sequence or array in which each further term is defined as a function of the preceding terms

Also known as recursive formula · recursive prescription · recurrence formula

Instance of: type of relation
Subclass of: sequence
, mathematical expression
, functional equation
Part of: relation

Overview

From Wikipedia, the free encyclopedia · Read full article · Text CC BY-SA 4.0

In mathematics, a recurrence relation is an equation according to which the th term of a sequence is equal to some combination of the previous terms. Often, only previous terms of the sequence appear in the equation, for a parameter that is independent of ; this number is called the order of the relation. If the values of the first numbers in the sequence have been given, the rest of the sequence can be calculated by repeatedly applying the equation.

Overview

All data

36 statements · 17% with external sources · numbers in brackets are citations

Has characteristic: recursive definition
Opposite of: explicit formula
Different from: recursive definition
Contains: difference equation
Used by: recursive sequence

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26 identifiers linking recurrence relation across the web's reference databases

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statements

17%

externally sourced

Source last edited October 26, 2026. AIDb refreshes this page daily.

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AIDb. (2026). recurrence relation (Q740970). Retrieved from https://aidb.si/e/recurrence-relation-Q740970