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: http://en.wikipedia.org/wiki/Gamma_function

The equation that defines Gamma Function is

Following figure presents the graph of Gamma Function

And when

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

-->factorial(1)

ans =

1.

-->gamma(1)

ans =

1.

-->factorial(1.5)

!--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 :

factorial(1.5)

-->gamma(1.5)

ans =

0.8862269

-->sqrt(%pi)/2

ans =

0.8862269

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.

Theory about Gamma Function is very well described in Wikipedia: http://en.wikipedia.org/wiki/Gamma_function

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 thatThis 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

-->factorial(1)

ans =

1.

-->gamma(1)

ans =

1.

-->factorial(1.5)

!--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 :

factorial(1.5)

-->gamma(1.5)

ans =

0.8862269

-->sqrt(%pi)/2

ans =

0.8862269

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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