Factorial and Gamma Functions for VB

[kadghar]

Hi, I saw that Killer posted a simple Factorial Function that allows you to calculate up to 13!, well, you can use this for bigger numbers by changing the variable type.

Why is this?

You can use factorial on integers (that should be the input), the output could be a string or a double, anyway you will alwas have the factorial. The only restriction is in the input.

Yes, i mean this function works fine for values up to 170! or something like that:

Public Function Factorial(ByVal bNum As Integer) As Double
  Dim I As Double
  If bNum <= 0 Then Exit Function
  Factorial = 1
  For I = 1 To bNum
    Factorial = Factorial * I
  Next
End Function

Also VB can be used for making a little bit more complex functions like a Gamma.

What is a Gamma?

A Gamma Function is the generalization of the Factorial Function (this means you can use any positive number in it). If you use a Gamma for an integer, it'll give you the Factorial of the previus integer. i.e.:

G(5) = 4 ! = 24

The advantage is that even if you cannot have 4.25 ! , you can always have
G(5.25) = 35.2088612458766

Cool!!!

To obtain it, you can use many numerical methods. Here I used an old friend by Euler-Mascheroni.

Public Function Gamma(ByVal Dou1 As Double) As Double
    Dim I As Integer
    Dim Dou2 As Double
    Dim Dou3 As Double
 
    If Fix(Dou1) = Dou1 Then
        If Dou1 = 0 Or Dou1 = 1 Then
            Gamma = 1
            Exit Function
        Else
            Dou2 = 1
            For I = 1 To Dou1 - 1
                Dou2 = Dou2 * I
            Next
            Gamma = Dou2
            Exit Function
        End If
    ElseIf Dou1 > 3 Then
        Dou2 = 1
        For I = 1 To (Fix(Dou1) - 1)
            Dou2 = Dou2 * (Dou1 - 1)
            Dou1 = Dou1 - 1
        Next
        Dou3 = Exp(-0.57721566 * Dou1) / Dou1
        For I = 1 To 9999
            Dou3 = Dou3 * ((1 + (Dou1 / I)) ^ (-1)) * Exp(Dou1 / I)
        Next
        Dou3 = Dou2 * Dou3
        Gamma = Dou3
    Else
        Dou3 = Exp(-0.577215664901533 * Dou1) / Dou1
        For I = 1 To 9999
            Dou3 = Dou3 * ((1 + (Dou1 / I)) ^ (-1)) * Exp(Dou1 / I)
        Next
        Gamma = Dou3
    End If
End Function

I hope this could be of some use next time you're dealing with someones homework.

Kad