#include <boost/math/special_functions/hypergeometric_2F0.hpp>

namespace boost { namespace math {

template <class T1, class T2, class T3>
calculated-result-type hypergeometric_2F0(T1 a1, T2 a2, T3 z);

template <class T1, class T2, class T3, class Policy>
calculated-result-type hypergeometric_2F0(T1 a1, T2 a2, T3 z, const Policy&);

}}

Description

The function hypergeometric_2F0 returns the result of

The return type of these functions is computed using the result type calculation rules when T1 and T2 are different types.

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.

The functions return the result of domain_error whenever the result is undefined or complex. The valid domain for this function occurs only when one of a1 or a2 is a negative integer: ie the polynomial case.

Implementation

When a1 == a2 - 0.5 then the function is implemented in terms of the Hermite polynomial:

When both a1 and a2 are integers then the function is implemented in terms of the associated-Laguerre polynomial:

If the defining series is divergent, we use the continued fraction

Otherwise we use the defining series.