Monday, September 3, 2012

Gamma function

Last week I was teaching about combinatorial analysis and talking about factorial operator I remembered Gamma Function, this function is very useful in signal processing but particularly Gamma Function is equal to the factorial for non-negative integer numbers.

Theory about Gamma Function is very well described in Wikipedia:

The equation that defines Gamma Function is

Following figure presents the graph of Gamma Function

And when z is a non-negative integer is verified that

This consequence is because of the property

Typical values of Gamma function are

 In Scilab, there are both functions: gamma(.) and factorial(.), following are some examples of these functions

 ans  =


 ans  =


 !--error 10000
factorial: Wrong value for input argument #1: Scalar/vector/matrix/hypermatrix of positive integers expected.
at line      14 of function factorial called by : 

 ans  =


 ans  =


Look factorial(.) is not possible to be applied in a non-integer number, the same happens with negative numbers.

And gamma(.) in 1.5 is equal to sqrt(%pi)/2 verifying the correspondence presented in the typical values figure.

Obs.: all equations and figures that I posted in this text were got from the Wikipedia page.

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