Definitions for recurrence relation
re·cur·rence re·la·tion

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1. recurrence relationnoun

   an equation that recursively defines a sequence; each term of the sequence is defined as a function of the preceding terms.

WikipediaRate this definition:0.0 / 0 votes

1. Recurrence relation

   In mathematics, a recurrence relation is an equation according to which the n {\displaystyle n} th term of a sequence of numbers is equal to some combination of the previous terms. Often, only k {\displaystyle k} previous terms of the sequence appear in the equation, for a parameter k {\displaystyle k} that is independent of n {\displaystyle n} ; this number k {\displaystyle k} is called the order of the relation. If the values of the first k {\displaystyle k} numbers in the sequence have been given, the rest of the sequence can be calculated by repeatedly applying the equation. In linear recurrences, the nth term is equated to a linear function of the k {\displaystyle k} previous terms. A famous example is the recurrence for the Fibonacci numbers, where the order k {\displaystyle k} is two and the linear function merely adds the two previous terms. This example is a linear recurrence with constant coefficients, because the coefficients of the linear function (1 and 1) are constants that do not depend on n {\displaystyle n} . For these recurrences, one can express the general term of the sequence as a closed-form expression of n {\displaystyle n} . As well, linear recurrences with polynomial coefficients depending on n {\displaystyle n} are also important, because many common elementary and special functions have a Taylor series whose coefficients satisfy such a recurrence relation (see holonomic function). Solving a recurrence relation means obtaining a closed-form solution: a non-recursive function of n {\displaystyle n} . The concept of a recurrence relation can be extended to multidimensional arrays, that is, indexed families that are indexed by tuples of natural numbers.

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1. Recurrence relation

   In mathematics, a recurrence relation is an equation that recursively defines a sequence, once one or more initial terms are given: each further term of the sequence is defined as a function of the preceding terms. The term difference equation sometimes refers to a specific type of recurrence relation. However, "difference equation" is frequently used to refer to any recurrence relation. An example of a recurrence relation is the logistic map: with a given constant r; given the initial term x0 each subsequent term is determined by this relation. Some simply defined recurrence relations can have very complex behaviours, and they are a part of the field of mathematics known as nonlinear analysis. Solving a recurrence relation means obtaining a closed-form solution: a non-recursive function of n.

How to pronounce recurrence relation?

1. Alex

   US English

   David

   US English

   Mark

   US English

   Daniel

   British

   Libby

   British

   Mia

   British

   Karen

   Australian

   Hayley

   Australian

   Natasha

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   Indian

   Priya

   Indian

   Neerja

   Indian

   Zira

   US English

   Oliver

   British

   Wendy

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   Fred

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   Tessa

   South African

How to say recurrence relation in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of recurrence relation in Chaldean Numerology is: 3

2. Pythagorean Numerology

   The numerical value of recurrence relation in Pythagorean Numerology is: 6

References

1. ^ Wiktionary
   https://en.wiktionary.org/wiki/Recurrence_Relation
2. ^ Wikipedia
   https://en.wikipedia.org/wiki/Recurrence_Relation
3. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=recurrence relation