Is there mathematical gamma function in C#?

Question

I'd like to make a scientific calculator in C#, but I didn't find gamma function to calculate fractal factorials. The function's description is below: https://en.wikipedia.org/wiki/Gamma_function

How can I reach gamma function in C#?

Answer 1

Install the Math.NET package from nuget

Documentation on the Gamma Function : https://numerics.mathdotnet.com/Functions.html

Answer 2

The Math.NET package is indeed an easy way to get the gamma function. Please keep in mind that gamma(x) is equal to (x-1)!. So, gamma(4.1) = 6.813 while 4.1! = 27.932. To get 4.1! from gamma(4.1), you can multiply gamma(4.1) by 4.1, or simply take the gamma of 5.1 instead. (I see no need to show a bunch of digits of precision here.)

In C#:

using MathNet.Numerics; //at beginning of program

private double Factorial(double x)
{
    double r = x;
    r *= SpecialFunctions.Gamma(x);
    return r;
    //This could be simplified into: 
    //return x * SpecialFunctions.Gamma(x);
}

private double Factorial2(double x)
{
    double r;
    r = SpecialFunctions.Gamma(x + 1);
    return r;
}

If for some reason you don't want to use Math.Net, you can write your own gamma function as follows:

static int g = 7;
static double[] p = {0.99999999999980993, 676.5203681218851, -1259.1392167224028,
 771.32342877765313, -176.61502916214059, 12.507343278686905,
 -0.13857109526572012, 9.9843695780195716e-6, 1.5056327351493116e-7};

Complex MyGamma(Complex z)
{
    // Reflection formula
    if (z.Real < 0.5)
    {
        return Math.PI / (Complex.Sin(Math.PI * z) * MyGamma(1 - z));
    }
    else
    {
        z -= 1;
        Complex x = p[0];
        for (var i = 1; i < g + 2; i++)
        {
            x += p[i] / (z + i);
        }
        Complex t = z + g + 0.5;
        return Complex.Sqrt(2 * Math.PI) * (Complex.Pow(t, z + 0.5)) * Complex.Exp(-t) * x;
    }
}

Note that you can replace the data type Complex with double and the Complex. functions with Math. if you don't need complex numbers, like so:

double MyGammaDouble(double z)
{
    if (z < 0.5)
        return Math.PI / (Math.Sin(Math.PI * z) * MyGammaDouble(1 - z));
    z -= 1;
    double x = p[0];
    for (var i = 1; i < g + 2; i++)
        x += p[i] / (z + i);
    double t = z + g + 0.5;
    return Math.Sqrt(2 * Math.PI) * (Math.Pow(t, z + 0.5)) * Math.Exp(-t) * x;
}

This is from an old wiki page (which has been replaced) but is copied here.