All of the special functions in this library come in two overloaded forms, one with a final "policy" parameter, and one without. For example:

namespace boost{ namespace math{

template <class RealType, class Policy>
RealType tgamma(RealType, const Policy&);

template <class RealType>
RealType tgamma(RealType);

}} // namespaces

Normally, the second version is just a forwarding wrapper to the first like this:

template <class RealType>
inline RealType tgamma(RealType x)
{
   return tgamma(x, policies::policy<>());
}

So calling a special function with a specific policy is just a matter of defining the policy type to use and passing it as the final parameter. For example, suppose we want tgamma to behave in a C-compatible fashion and set ::errno when an error occurs, and never throw an exception:

#include <boost/math/special_functions/gamma.hpp>
using boost::math::tgamma;

// Define the policy to use:
using namespace boost::math::policies; // may be convenient, or

using boost::math::policies::policy;
// Types of error whose action can be altered by policies:.
using boost::math::policies::evaluation_error;
using boost::math::policies::domain_error;
using boost::math::policies::overflow_error;
using boost::math::policies::domain_error;
using boost::math::policies::pole_error;
// Actions on error (in enum error_policy_type):
using boost::math::policies::errno_on_error;
using boost::math::policies::ignore_error;
using boost::math::policies::throw_on_error;
using boost::math::policies::user_error;

typedef policy<
   domain_error<errno_on_error>,
   pole_error<errno_on_error>,
   overflow_error<errno_on_error>,
   evaluation_error<errno_on_error>
> c_policy;
//
// Now use the policy when calling tgamma:

// http://msdn.microsoft.com/en-us/library/t3ayayh1.aspx 
// Microsoft errno declared in STDLIB.H as "extern int errno;" 

int main()
{
   errno = 0; // Reset.
   cout << "Result of tgamma(30000) is: "
      << tgamma(30000, c_policy()) << endl; // Too big parameter
   cout << "errno = " << errno << endl; // errno 34 Numerical result out of range.
   cout << "Result of tgamma(-10) is: "
      << boost::math::tgamma(-10, c_policy()) << endl; // Negative parameter.
   cout << "errno = " << errno << endl; // error 33 Numerical argument out of domain.
} // int main()

which outputs:

Result of tgamma(30000) is: 1.#INF
errno = 34
Result of tgamma(-10) is: 1.#QNAN
errno = 33

Alternatively, for ad hoc use, we can use the make_policy helper function to create a policy for us: this usage is more verbose, so is probably only preferred when a policy is going to be used once only:

#include <boost/math/special_functions/gamma.hpp>
using boost::math::tgamma;

int main()
{
   // using namespace boost::math::policies; // or
   using boost::math::policies::errno_on_error;
   using boost::math::policies::make_policy;
   using boost::math::policies::pole_error;
   using boost::math::policies::domain_error;
   using boost::math::policies::overflow_error;
   using boost::math::policies::evaluation_error;

   errno = 0;
   std::cout << "Result of tgamma(30000) is: "
      << boost::math::tgamma(
         30000,
         make_policy(
            domain_error<errno_on_error>(),
            pole_error<errno_on_error>(),
            overflow_error<errno_on_error>(),
            evaluation_error<errno_on_error>()
         )
      ) << std::endl;
   // Check errno was set:
   std::cout << "errno = " << errno << std::endl;
   // and again with evaluation at a pole:
   std::cout << "Result of tgamma(-10) is: "
      << boost::math::tgamma(
         -10,
         make_policy(
            domain_error<errno_on_error>(),
            pole_error<errno_on_error>(),
            overflow_error<errno_on_error>(),
            evaluation_error<errno_on_error>()
         )
      ) << std::endl;
   // Check errno was set:
   std::cout << "errno = " << errno << std::endl;
}