Mirage Source

    Public Function Factorial(ByVal n As Integer) As Decimal
        Dim i As Integer
        Dim fac As Object
        fac = 1
        i = n

        If n = 0 Then
            Factorial = 1
        Else

            Do While i > 1
                fac *= i
                i -= 1
            Loop

            Factorial = fac
        End If

    End Function

    Public Function nCr(ByVal n As Integer, ByVal k As Integer) As Long
        nCr = Factorial(n) / (Factorial(k) * Factorial(n - k))
    End Function

    Public Function FracPwr(ByVal x As Integer, ByVal y As Integer, ByVal z As Integer) As Double
        Dim raise As Double
        raise = Math.Pow(z, -1)
        FracPwr = Math.Pow(Math.Pow(x, y), raise)
    End Function

    Public Sub TanSeq(ByVal n As Integer)
        Dim j, k As Integer
        Dim Term1, Term2 As Object
        Term2 = 0

        If n Mod 2 = 0 Then
            Exit Sub
        End If

        T(n) = Math.Pow(2, n)

        For j = 1 To n
            Term1 = 0
            For k = 0 To (n - j)
                Term1 += nCr(n + 1, k)
            Next
            Term2 += Math.Pow(-1, j + n + 1) * Math.Pow(j, n) * Term1
        Next

        If Term2 < 0 Then
            Term2 *= -1
        End If

        T(n) *= (Term2 / Math.Pow(2, n))

    End Sub

    Public Function chen(ByVal k As Integer) As Double
        Dim q, r As Double

        If k Mod 4 <> 0 Then
            q = k / 4
            r = k / 2
            chen = FracPwr(-1, k, 4) / FracPwr(2, k, 2) * 1
        Else
            chen = 0
        End If

    End Function

    Public Function Bernoulli(ByVal x As Integer, ByVal n As Integer) As Double
        Dim i, j As Integer
        Dim Bern As Double
        B(0) = 1
        Bern = 0

        For i = 0 To n
            If i > 0 Then
                For j = (i - 1) To 0
                    Bern += B(j) * (Math.Pow(x, j) / Factorial(j))
                Next
                B(i + 1) = Bern
            Else
                B(i + 1) = B(i) * (Math.Pow(x, i) / Factorial(i))
            End If
        Next

        Bernoulli = B(n)
    End Function

        Public Sub EulerianGen(ByVal n As Integer, ByVal m As Integer)
        Dim i, k As Integer
        i = 0

        'Generate for n = 1 to 3 (All can be done this way, but recurrance is easier.
        If n = 0 Or n = 1 Or n = 2 Or n = 3 Then

            For k = 0 To m
                i += (Math.Pow(-1, k) * nCr(n + 1, k) * Math.Pow(m + 1 - k, n))
            Next

            Eulerian(n, m) = i
            Exit Sub

        End If

        'Recurrance can only be done for n > 3
        If m <> 0 Then
            Eulerian(n, m) = (n - m) * Eulerian(n - 1, m - 1) + (m + 1) * Eulerian(n - 1, m)
        Else
            Eulerian(n, m) = 1
        End If

    End Sub

    Public Sub StirlingGen(ByVal n As Integer, ByVal k As Integer)

        'If n and k are the same, then the Stirling Number is one.
        If n = k Then
            Stirling(n, k) = 1
            Exit Sub
        End If

        'If k is one, then the Stirling Number is also one.
        If k = 1 And n = Not 0 Then
            Stirling(n, k) = 1
            Exit Sub
        End If

        'If k is 0 and n is not 0 then the stirling number is 0.
        If k = 0 And Not n = 0 Then
            Stirling(n, k) = 0
            Exit Sub
        End If

        'If k > n then 0
        If k > n Then
            Stirling(n, k) = 0
            Exit Sub
        End If

        'Recurrance formula as long as k <= n
        If Not k > n Then
            Stirling(n, k) = Stirling(n - 1, k - 1) + k * Stirling(n - 1, k)
        Else
            Stirling(n, k) = 0
        End If

    End Sub

a = a + 1

a += 1