public static Complex Gamma(Complex z, int order = 10)
{
// ∫[0,∞] t^-z e^-t dt.
var integral = Complex.Zero;
double dt = 1.0 / order;
double t = 0;
for (int n = 0; n <= order; ++n)
{
integral += Complex.Pow(t, z) * Functions.Exp(-t);
t += dt;
}
return(integral);
}
/// <summary>
/// Returns e raised to the power specified by a complex number.
/// </summary>
/// <param name="value">A complex number that specifies a power.</param>
/// <returns>The number e raised to the power value.</returns>
public static Complex Exp(Complex value)
{
double e = Functions.Exp(value.A);
return(new Complex(e * Functions.Cos(value.B), e * Functions.Sin(value.B)));
}
