| Home | Libraries | People | FAQ | More

### Falling Factorial

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

    namespace boost{ namespace math{

    template <class T>
    calculated-result-type falling_factorial(T x, unsigned i);

    template <class T, class Policy>
    calculated-result-type falling_factorial(T x, unsigned i, const Policy&);

    }} // namespaces

Returns the falling factorial of x and i:

> falling_factorial(x, i) = x(x-1)(x-2)(x-3)...(x-i+1)

Note that this function is only defined for positive i, hence the `unsigned` second argument. Argument x can be either positive or negative however.

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 return type of these functions is computed using the result type calculation rules: the type of the result is `double` if T is an integer type, otherwise the type of the result is T.

##### Accuracy

The accuracy will be the same as the tgamma_delta_ratio function.

##### Testing

The spot tests for the falling factorials use data generated by functions.wolfram.com.

##### Implementation

Rising and falling factorials are implemented as ratios of gamma functions using tgamma_delta_ratio. Optimisations for small integer arguments are handled internally by that function.