A recurrence relation is a functional relationship between the independent variable x, the dependent variable f(x), and the differences between different orders of f. (x). A difference equation is another name for a recurrence relation, and we'll use both names interchangeably.

The majority of general recurrence relations result in concern linear recurrences, which are recurrence relations in which the nth term is linear in regard to the preceding terms. Linear recurrences with constant coefficients and linear recurrences with polynomial coefficients are two of the most essential types of recurrences.

This is because the sequence's general term may be expressed as a closed-form expression of the term's index in the first instance. This is because many common elementary and special functions contain a Taylor series whose coefficients meet this recurrence relation in the second instance.

In this “Recurrence Relations - Mathematical Foundation of Computer Science” you will learn about the following topics:

- Recursive Definition of Sequences
- Differencing and Summation
- Solution of Linear Recursive Relation
- Solution of Non-linear Recurrence Relation.

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This article Recurrence Relations - Mathematical Foundation of Computer Science is contributed by Namrata Chaudhary, a student of Lumbini Engineering College (LEC).

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