Example of recursive functions, MATLAB in Mathematics

Example of Recursive functions:

This definition is recursive as a factorial is defined in terms of the other factorial. There are two parts to any recursive definition: the common or inductive case, and the base case. We say that in common the factorial of n is defined as n multiplied by the factorial of (n - 1), but the base case is that the factorial of 1 is 1. The base case stops the recursion.

For illustration,

3! = 3 * 2!

2! = 2 * 1!

          1! = 1

= 2

= 6

The way it works is that 3! is defined in terms of the other factorial, as 3 * 2!. This expression cannot yet be computed, as first we have to find out the value of 2!. Therefore, in trying to compute the expression 3 * 2!, interruption by recursive definition occurs. According to the definition, 2! be 2 * 1!. And again, the expression 2 * 1! cannot yet be computed as first we have to find the value of 1!. According to the definition, 1! be 1. As we now know what 1! is, we can carry on with the expression which was just being computed; now we know that 2 * 1! is 2 * 1, or 2. Therefore, now we can finish the earlier expression which was being computed; now we know that 3 * 2! is 3 * 2, or 6.

This is the approach that recursion always works. By recursion, the expressions are place on hold with interruption of the common case of the recursive definition. This keeps occurring until finally the base case of the recursive definition applies. This at last stops the recursion, and then the expressions which were put on hold are computed in the reverse order. In this situation, first the computationof 2 * 1! was done, and then 3 * 2!.

There should always be a base case to end the recursion, and the base case should be reached at several points. Or else, infinite recursion would occur (theoretically, though MATLAB will stop the recursion ultimately).

Posted Date: 10/22/2012 1:29:26 AM | Location : United States







Related Discussions:- Example of recursive functions, Assignment Help, Ask Question on Example of recursive functions, Get Answer, Expert's Help, Example of recursive functions Discussions

Write discussion on Example of recursive functions
Your posts are moderated
Related Questions
Strings as Vectors: The Strings are considered as vectors of characters-or in another words, a vector in which each and every element is a single character-so numerous vector

Give the formula for a rational function that has a hole at x=7 & vertical asmptote at x=-3/2

Standard Deviation The standard deviation is the square root of variance: The built-in function in a MATLAB for the standard deviation is known as std; the standard dev

Example of Recursive functions: This definition is recursive as a factorial is defined in terms of the other factorial. There are two parts to any recursive definition: the co

Common form of the switch statement: The common form of the switch statement is as shown below:   switch switch_expression   case caseexp1    action1   case cas

Logical Vectors: The relational operators can also be used with the vectors and matrices. For illustration, let's say that there is a vector, and we want to compare each eleme

fprintf function - File function: The fprintf function really returns the number of bytes which was written to the file, therefore if you do not want to see that number, suppr

Applications of Customized Strings: Labels, Prompts, Arguments to Functions: The one of very useful application of this is to involve numbers in strings that are used to plot

Animation: In this part we will observe a couple of ways to animate a plot. These are visuals, therefore the outcomes can't really be shown here; it is essential to type these

Program of built-in factorial function: Calling this function yields similar result as the built-in factorial function: >> fact(5) ans =   120 >> factorial(