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Double Factorial

#include <boost/math/special_functions/factorials.hpp>

namespace boost{ namespace math{

template <class T>
T double_factorial(unsigned i);

template <class T, class Policy>
T double_factorial(unsigned i, const Policy&);

}} // namespaces

Returns i!!.

The final Policy argument is optional and can be used to control the behaviour of the function: how it handles errors, what level of precision to use etc. Refer to the policy documentation for more details.

May return the result of overflow_error if the result is too large to represent in type T. The implementation is designed to be optimised for small i where table lookup of i! is possible.

Accuracy

The implementation uses a trivial adaptation of the factorial function, so error rates should be no more than a couple of epsilon higher.

Testing

The spot tests for the double factorial use data generated by functions.wolfram.com.

Implementation

The double factorial is implemented in terms of the factorial and gamma functions using the relations:

(2n)!! = 2n * n!

(2n+1)!! = (2n+1)! / (2n n!)

and

(2n-1)!! = Γ((2n+1)/2) * 2n / sqrt(pi)


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