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Hypergeometric 0F1

#include <boost/math/special_functions/hypergeometric_0F1.hpp>

namespace boost { namespace math {

template <class T1, class T2>
calculated-result-type hypergeometric_0F1(T1 b, T2 z);

template <class T1, class T2, class Policy>
calculated-result-type hypergeometric_0F1(T1 b, T2 z, const Policy&);

}} // namespaces

The function hypergeometric_0F1 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. This occurs only when b is an integer <= 0.


The function is implemented via its defining series wherever convergent.

For a divergent series we use the continued fraction as long as the result is not too small:

and one of the Bessel function relations otherwise: