Need help putting integral function into C#

Question

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

alt text

Thanks

Answer 1

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".

Need help putting integral function into C#

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