# recursion

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Related to recursion: recursion formula, Tail recursion

## recursion

[ri′kər·zhən]
(computer science)
A technique in which an apparently circular process is used to perform an iterative process.

## recursion

(mathematics, programming)
When a function (or procedure) calls itself. Such a function is called "recursive". If the call is via one or more other functions then this group of functions are called "mutually recursive".

If a function will always call itself, however it is called, then it will never terminate. Usually however, it first performs some test on its arguments to check for a "base case" - a condition under which it can return a value without calling itself.

The canonical example of a recursive function is factorial:

factorial 0 = 1 factorial n = n * factorial (n-1)

Functional programming languages rely heavily on recursion, using it where a procedural language would use iteration.

See also recursion, recursive definition, tail recursion.

## recursion

In programming, the ability of a subroutine or program module to call itself. It is used to write routines that solve problems by repeatedly processing the output of the same process. See recurse subdirectories, circular reference and recursive descent parser.
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n](z) of Legendre's equation (1) using backward recursion.
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In order to prove our main result, we used the recursion already established for [Nara.

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