internal static double PowerOverFactorial(double x, double nu)
{
if (nu < 16.0)
{
return(Math.Pow(x, nu) / AdvancedMath.Gamma(nu + 1.0));
}
else
{
return(Stirling.PowerFactor(x, nu));
}
}
// This function computes x^n / n! or x^{\nu} / \Gamma(\nu + 1), which can easily become
// Infinity/Infinity=NaN for large n if computed naively.
internal static double PowerOverFactorial(double x, int n)
{
if (n <= 16)
{
// For maximum range, we should evaluate this using Lanczos, but
// since we know we don't call it for x large enough for x^n to overflow,
// this is safer and faster.
return(MoreMath.Pow(x, n) / AdvancedIntegerMath.Factorial(n));
}
else
{
return(Stirling.PowerFactor(x, n));
}
}