Need help putting integral function into C#

Hi, I’m trying to put this function into one of my scripts, but I don’t know how to do the integrals in C#. Hopefully someone here can help



This is off topic since it’s a pure mathematical / computer science question and not related to Unity. Anyways, as you can actually read here:

These integrals cannot be expressed in
terms of elementary functions […]
however, many numerical approximations
are known

Specifically the expansion into an infinite series. Of course we can not calculate an infinite series however we can simply choose a certain number of terms and stop.

Something like that might work

public static double Phi(double x, int n)
    double sum = 0;
    double x2 = x*x;
    double nom = x;
    double denom = 1;
    double c = 1;
    for (int i = 0; i < n; i++)
        sum += nom / denom;
        c += 2;
        nom *= x2;
        denom *= c;
    return 0.5 + sum * System.Math.Exp(-x2*0.5) / System.Math.Sqrt(2 * System.Math.PI);

Unless I made a mistake this should calculate the “nth” approximation of the Phi function. You have to decide how large you choose your “n”.