Accord.Math.Gamma.Trigamma C# (CSharp) Method

        public static double Trigamma(double x)
        {
            double a = 0.0001;
            double b = 5.0;
            double b2 = 0.1666666667;
            double b4 = -0.03333333333;
            double b6 = 0.02380952381;
            double b8 = -0.03333333333;
            double value;
            double y;
            double z;

            // Check the input.
            if (x <= 0.0)
            {
                throw new ArgumentException("The input parameter x must be positive.", "x");
            }

            z = x;

            // Use small value approximation if X <= A.
            if (x <= a)
            {
                value = 1.0 / x / x;
                return value;
            }

            // Increase argument to ( X + I ) >= B.
            value = 0.0;

            while (z < b)
            {
                value = value + 1.0 / z / z;
                z = z + 1.0;
            }

            // Apply asymptotic formula if argument is B or greater.
            y = 1.0 / z / z;

            value = value + 0.5 *
                y + (1.0
              + y * (b2
              + y * (b4
              + y * (b6
              + y * b8)))) / z;

            return value;
        }