/// Complement of incomplete gamma function Q(a,x), a > 0, x >= 0.
/// Q(a,x) = (1/gamma(a)) integral (x to inf) { exp(-t) t^(a-1) dt }
/// @param a first argument, a > 0
/// @param x second argument, x >= 0
/// @return Q(a,x)
/// @throw if input arguments have a <= 0 or x < 0
double compIncompGamma(const double& a, const double& x) throw(Exception)
{
try {
if(x < 0) GPSTK_THROW(Exception("Negative first argument"));
if(a <= 0) GPSTK_THROW(Exception("Non-positive second argument"));
if(x < a+1.0)
return (1.0 - seriesIncompGamma(a,x));
else
return contfracIncompGamma(a,x);
}
catch(Exception& e) { GPSTK_RETHROW(e); }
}
/// Complement of incomplete gamma function Q(a,x), a > 0, x >= 0.
/// Q(a,x) = (1/gamma(a)) integral (x to inf) { exp(-t) t^(a-1) dt }
/// @param double a first argument, a > 0
/// @param double x second argument, x >= 0
/// @return Q(a,x)
/// @throw if input arguments have a <= 0 or x < 0
double compIncompGamma(const double& a, const double& x) throw(Exception)
{
if(x < 0) {
Exception e("Negative first argument in compIncompGamma()");
GPSTK_THROW(e);
}
if(a <= 0) {
Exception e("Non-positive second argument in compIncompGamma()");
GPSTK_THROW(e);
}
if(x < a+1.0)
return (1.0 - seriesIncompGamma(a,x));
else
return contfracIncompGamma(a,x);
}