rekurence

Rekurence, also known as recurrence, is a concept in mathematics and computer science that refers to the repetition of an item or sequence in a pattern. It is often used to describe the behavior of functions, sequences, or algorithms that repeat themselves in a predictable manner.

In mathematics, a recurrence relation is an equation that recursively defines a sequence, where each term is defined as a function of its preceding terms. For example, the Fibonacci sequence is defined by the recurrence relation F(n) = F(n-1) + F(n-2), with initial conditions F(0) = 0 and F(1) = 1.

In computer science, recurrence is used to describe the repetition of a function or algorithm within itself. This is often seen in recursive functions, where a function calls itself with a modified argument until a base case is reached. For example, the factorial function is defined recursively as n! = n * (n-1)!, with the base case 0! = 1.

Rekurence is a fundamental concept in both mathematics and computer science, with applications ranging from number theory and combinatorics to algorithm design and analysis. Understanding rekurence is essential for solving a wide range of problems in these fields.