%PDF-
%PDF-
Mini Shell
Mini Shell
// math_fwd.hpp
// TODO revise completely for new distribution classes.
// Copyright Paul A. Bristow 2006.
// Copyright John Maddock 2006.
// Use, modification and distribution are subject to the
// Boost Software License, Version 1.0.
// (See accompanying file LICENSE_1_0.txt
// or copy at http://www.boost.org/LICENSE_1_0.txt)
// Omnibus list of forward declarations of math special functions.
// IT = Integer type.
// RT = Real type (built-in floating-point types, float, double, long double) & User Defined Types
// AT = Integer or Real type
#ifndef BOOST_MATH_SPECIAL_MATH_FWD_HPP
#define BOOST_MATH_SPECIAL_MATH_FWD_HPP
#ifdef _MSC_VER
#pragma once
#endif
#include <vector>
#include <complex>
#include <type_traits>
#include <boost/math/special_functions/detail/round_fwd.hpp>
#include <boost/math/tools/promotion.hpp> // for argument promotion.
#include <boost/math/policies/policy.hpp>
#define BOOST_NO_MACRO_EXPAND /**/
namespace boost
{
namespace math
{ // Math functions (in roughly alphabetic order).
// Beta functions.
template <class RT1, class RT2>
tools::promote_args_t<RT1, RT2>
beta(RT1 a, RT2 b); // Beta function (2 arguments).
template <class RT1, class RT2, class A>
tools::promote_args_t<RT1, RT2, A>
beta(RT1 a, RT2 b, A x); // Beta function (3 arguments).
template <class RT1, class RT2, class RT3, class Policy>
tools::promote_args_t<RT1, RT2, RT3>
beta(RT1 a, RT2 b, RT3 x, const Policy& pol); // Beta function (3 arguments).
template <class RT1, class RT2, class RT3>
tools::promote_args_t<RT1, RT2, RT3>
betac(RT1 a, RT2 b, RT3 x);
template <class RT1, class RT2, class RT3, class Policy>
tools::promote_args_t<RT1, RT2, RT3>
betac(RT1 a, RT2 b, RT3 x, const Policy& pol);
template <class RT1, class RT2, class RT3>
tools::promote_args_t<RT1, RT2, RT3>
ibeta(RT1 a, RT2 b, RT3 x); // Incomplete beta function.
template <class RT1, class RT2, class RT3, class Policy>
tools::promote_args_t<RT1, RT2, RT3>
ibeta(RT1 a, RT2 b, RT3 x, const Policy& pol); // Incomplete beta function.
template <class RT1, class RT2, class RT3>
tools::promote_args_t<RT1, RT2, RT3>
ibetac(RT1 a, RT2 b, RT3 x); // Incomplete beta complement function.
template <class RT1, class RT2, class RT3, class Policy>
tools::promote_args_t<RT1, RT2, RT3>
ibetac(RT1 a, RT2 b, RT3 x, const Policy& pol); // Incomplete beta complement function.
template <class T1, class T2, class T3, class T4>
tools::promote_args_t<T1, T2, T3, T4>
ibeta_inv(T1 a, T2 b, T3 p, T4* py);
template <class T1, class T2, class T3, class T4, class Policy>
tools::promote_args_t<T1, T2, T3, T4>
ibeta_inv(T1 a, T2 b, T3 p, T4* py, const Policy& pol);
template <class RT1, class RT2, class RT3>
tools::promote_args_t<RT1, RT2, RT3>
ibeta_inv(RT1 a, RT2 b, RT3 p); // Incomplete beta inverse function.
template <class RT1, class RT2, class RT3, class Policy>
tools::promote_args_t<RT1, RT2, RT3>
ibeta_inv(RT1 a, RT2 b, RT3 p, const Policy&); // Incomplete beta inverse function.
template <class RT1, class RT2, class RT3>
tools::promote_args_t<RT1, RT2, RT3>
ibeta_inva(RT1 a, RT2 b, RT3 p); // Incomplete beta inverse function.
template <class RT1, class RT2, class RT3, class Policy>
tools::promote_args_t<RT1, RT2, RT3>
ibeta_inva(RT1 a, RT2 b, RT3 p, const Policy&); // Incomplete beta inverse function.
template <class RT1, class RT2, class RT3>
tools::promote_args_t<RT1, RT2, RT3>
ibeta_invb(RT1 a, RT2 b, RT3 p); // Incomplete beta inverse function.
template <class RT1, class RT2, class RT3, class Policy>
tools::promote_args_t<RT1, RT2, RT3>
ibeta_invb(RT1 a, RT2 b, RT3 p, const Policy&); // Incomplete beta inverse function.
template <class T1, class T2, class T3, class T4>
tools::promote_args_t<T1, T2, T3, T4>
ibetac_inv(T1 a, T2 b, T3 q, T4* py);
template <class T1, class T2, class T3, class T4, class Policy>
tools::promote_args_t<T1, T2, T3, T4>
ibetac_inv(T1 a, T2 b, T3 q, T4* py, const Policy& pol);
template <class RT1, class RT2, class RT3>
tools::promote_args_t<RT1, RT2, RT3>
ibetac_inv(RT1 a, RT2 b, RT3 q); // Incomplete beta complement inverse function.
template <class RT1, class RT2, class RT3, class Policy>
tools::promote_args_t<RT1, RT2, RT3>
ibetac_inv(RT1 a, RT2 b, RT3 q, const Policy&); // Incomplete beta complement inverse function.
template <class RT1, class RT2, class RT3>
tools::promote_args_t<RT1, RT2, RT3>
ibetac_inva(RT1 a, RT2 b, RT3 q); // Incomplete beta complement inverse function.
template <class RT1, class RT2, class RT3, class Policy>
tools::promote_args_t<RT1, RT2, RT3>
ibetac_inva(RT1 a, RT2 b, RT3 q, const Policy&); // Incomplete beta complement inverse function.
template <class RT1, class RT2, class RT3>
tools::promote_args_t<RT1, RT2, RT3>
ibetac_invb(RT1 a, RT2 b, RT3 q); // Incomplete beta complement inverse function.
template <class RT1, class RT2, class RT3, class Policy>
tools::promote_args_t<RT1, RT2, RT3>
ibetac_invb(RT1 a, RT2 b, RT3 q, const Policy&); // Incomplete beta complement inverse function.
template <class RT1, class RT2, class RT3>
tools::promote_args_t<RT1, RT2, RT3>
ibeta_derivative(RT1 a, RT2 b, RT3 x); // derivative of incomplete beta
template <class RT1, class RT2, class RT3, class Policy>
tools::promote_args_t<RT1, RT2, RT3>
ibeta_derivative(RT1 a, RT2 b, RT3 x, const Policy& pol); // derivative of incomplete beta
// Binomial:
template <class T, class Policy>
T binomial_coefficient(unsigned n, unsigned k, const Policy& pol);
template <class T>
T binomial_coefficient(unsigned n, unsigned k);
// erf & erfc error functions.
template <class RT> // Error function.
tools::promote_args_t<RT> erf(RT z);
template <class RT, class Policy> // Error function.
tools::promote_args_t<RT> erf(RT z, const Policy&);
template <class RT>// Error function complement.
tools::promote_args_t<RT> erfc(RT z);
template <class RT, class Policy>// Error function complement.
tools::promote_args_t<RT> erfc(RT z, const Policy&);
template <class RT>// Error function inverse.
tools::promote_args_t<RT> erf_inv(RT z);
template <class RT, class Policy>// Error function inverse.
tools::promote_args_t<RT> erf_inv(RT z, const Policy& pol);
template <class RT>// Error function complement inverse.
tools::promote_args_t<RT> erfc_inv(RT z);
template <class RT, class Policy>// Error function complement inverse.
tools::promote_args_t<RT> erfc_inv(RT z, const Policy& pol);
// Polynomials:
template <class T1, class T2, class T3>
tools::promote_args_t<T1, T2, T3>
legendre_next(unsigned l, T1 x, T2 Pl, T3 Plm1);
template <class T>
tools::promote_args_t<T>
legendre_p(int l, T x);
template <class T>
tools::promote_args_t<T>
legendre_p_prime(int l, T x);
template <class T, class Policy>
inline std::vector<T> legendre_p_zeros(int l, const Policy& pol);
template <class T>
inline std::vector<T> legendre_p_zeros(int l);
template <class T, class Policy>
typename std::enable_if<policies::is_policy<Policy>::value, tools::promote_args_t<T>>::type
legendre_p(int l, T x, const Policy& pol);
template <class T, class Policy>
inline typename std::enable_if<policies::is_policy<Policy>::value, tools::promote_args_t<T>>::type
legendre_p_prime(int l, T x, const Policy& pol);
template <class T>
tools::promote_args_t<T>
legendre_q(unsigned l, T x);
template <class T, class Policy>
typename std::enable_if<policies::is_policy<Policy>::value, tools::promote_args_t<T>>::type
legendre_q(unsigned l, T x, const Policy& pol);
template <class T1, class T2, class T3>
tools::promote_args_t<T1, T2, T3>
legendre_next(unsigned l, unsigned m, T1 x, T2 Pl, T3 Plm1);
template <class T>
tools::promote_args_t<T>
legendre_p(int l, int m, T x);
template <class T, class Policy>
tools::promote_args_t<T>
legendre_p(int l, int m, T x, const Policy& pol);
template <class T1, class T2, class T3>
tools::promote_args_t<T1, T2, T3>
laguerre_next(unsigned n, T1 x, T2 Ln, T3 Lnm1);
template <class T1, class T2, class T3>
tools::promote_args_t<T1, T2, T3>
laguerre_next(unsigned n, unsigned l, T1 x, T2 Pl, T3 Plm1);
template <class T>
tools::promote_args_t<T>
laguerre(unsigned n, T x);
template <class T, class Policy>
tools::promote_args_t<T>
laguerre(unsigned n, unsigned m, T x, const Policy& pol);
template <class T1, class T2>
struct laguerre_result
{
using type = typename std::conditional<
policies::is_policy<T2>::value,
typename tools::promote_args<T1>::type,
typename tools::promote_args<T2>::type
>::type;
};
template <class T1, class T2>
typename laguerre_result<T1, T2>::type
laguerre(unsigned n, T1 m, T2 x);
template <class T>
tools::promote_args_t<T>
hermite(unsigned n, T x);
template <class T, class Policy>
tools::promote_args_t<T>
hermite(unsigned n, T x, const Policy& pol);
template <class T1, class T2, class T3>
tools::promote_args_t<T1, T2, T3>
hermite_next(unsigned n, T1 x, T2 Hn, T3 Hnm1);
template<class T1, class T2, class T3>
tools::promote_args_t<T1, T2, T3> chebyshev_next(T1 const & x, T2 const & Tn, T3 const & Tn_1);
template <class Real, class Policy>
tools::promote_args_t<Real>
chebyshev_t(unsigned n, Real const & x, const Policy&);
template<class Real>
tools::promote_args_t<Real> chebyshev_t(unsigned n, Real const & x);
template <class Real, class Policy>
tools::promote_args_t<Real>
chebyshev_u(unsigned n, Real const & x, const Policy&);
template<class Real>
tools::promote_args_t<Real> chebyshev_u(unsigned n, Real const & x);
template <class Real, class Policy>
tools::promote_args_t<Real>
chebyshev_t_prime(unsigned n, Real const & x, const Policy&);
template<class Real>
tools::promote_args_t<Real> chebyshev_t_prime(unsigned n, Real const & x);
template<class Real, class T2>
Real chebyshev_clenshaw_recurrence(const Real* const c, size_t length, const T2& x);
template <class T1, class T2>
std::complex<tools::promote_args_t<T1, T2>>
spherical_harmonic(unsigned n, int m, T1 theta, T2 phi);
template <class T1, class T2, class Policy>
std::complex<tools::promote_args_t<T1, T2>>
spherical_harmonic(unsigned n, int m, T1 theta, T2 phi, const Policy& pol);
template <class T1, class T2>
tools::promote_args_t<T1, T2>
spherical_harmonic_r(unsigned n, int m, T1 theta, T2 phi);
template <class T1, class T2, class Policy>
tools::promote_args_t<T1, T2>
spherical_harmonic_r(unsigned n, int m, T1 theta, T2 phi, const Policy& pol);
template <class T1, class T2>
tools::promote_args_t<T1, T2>
spherical_harmonic_i(unsigned n, int m, T1 theta, T2 phi);
template <class T1, class T2, class Policy>
tools::promote_args_t<T1, T2>
spherical_harmonic_i(unsigned n, int m, T1 theta, T2 phi, const Policy& pol);
// Elliptic integrals:
template <class T1, class T2, class T3>
tools::promote_args_t<T1, T2, T3>
ellint_rf(T1 x, T2 y, T3 z);
template <class T1, class T2, class T3, class Policy>
tools::promote_args_t<T1, T2, T3>
ellint_rf(T1 x, T2 y, T3 z, const Policy& pol);
template <class T1, class T2, class T3>
tools::promote_args_t<T1, T2, T3>
ellint_rd(T1 x, T2 y, T3 z);
template <class T1, class T2, class T3, class Policy>
tools::promote_args_t<T1, T2, T3>
ellint_rd(T1 x, T2 y, T3 z, const Policy& pol);
template <class T1, class T2>
tools::promote_args_t<T1, T2>
ellint_rc(T1 x, T2 y);
template <class T1, class T2, class Policy>
tools::promote_args_t<T1, T2>
ellint_rc(T1 x, T2 y, const Policy& pol);
template <class T1, class T2, class T3, class T4>
tools::promote_args_t<T1, T2, T3, T4>
ellint_rj(T1 x, T2 y, T3 z, T4 p);
template <class T1, class T2, class T3, class T4, class Policy>
tools::promote_args_t<T1, T2, T3, T4>
ellint_rj(T1 x, T2 y, T3 z, T4 p, const Policy& pol);
template <class T1, class T2, class T3>
tools::promote_args_t<T1, T2, T3>
ellint_rg(T1 x, T2 y, T3 z);
template <class T1, class T2, class T3, class Policy>
tools::promote_args_t<T1, T2, T3>
ellint_rg(T1 x, T2 y, T3 z, const Policy& pol);
template <typename T>
tools::promote_args_t<T> ellint_2(T k);
template <class T1, class T2>
tools::promote_args_t<T1, T2> ellint_2(T1 k, T2 phi);
template <class T1, class T2, class Policy>
tools::promote_args_t<T1, T2> ellint_2(T1 k, T2 phi, const Policy& pol);
template <typename T>
tools::promote_args_t<T> ellint_1(T k);
template <class T1, class T2>
tools::promote_args_t<T1, T2> ellint_1(T1 k, T2 phi);
template <class T1, class T2, class Policy>
tools::promote_args_t<T1, T2> ellint_1(T1 k, T2 phi, const Policy& pol);
template <typename T>
tools::promote_args_t<T> ellint_d(T k);
template <class T1, class T2>
tools::promote_args_t<T1, T2> ellint_d(T1 k, T2 phi);
template <class T1, class T2, class Policy>
tools::promote_args_t<T1, T2> ellint_d(T1 k, T2 phi, const Policy& pol);
template <class T1, class T2>
tools::promote_args_t<T1, T2> jacobi_zeta(T1 k, T2 phi);
template <class T1, class T2, class Policy>
tools::promote_args_t<T1, T2> jacobi_zeta(T1 k, T2 phi, const Policy& pol);
template <class T1, class T2>
tools::promote_args_t<T1, T2> heuman_lambda(T1 k, T2 phi);
template <class T1, class T2, class Policy>
tools::promote_args_t<T1, T2> heuman_lambda(T1 k, T2 phi, const Policy& pol);
namespace detail{
template <class T, class U, class V>
struct ellint_3_result
{
using type = typename std::conditional<
policies::is_policy<V>::value,
tools::promote_args_t<T, U>,
tools::promote_args_t<T, U, V>
>::type;
};
} // namespace detail
template <class T1, class T2, class T3>
typename detail::ellint_3_result<T1, T2, T3>::type ellint_3(T1 k, T2 v, T3 phi);
template <class T1, class T2, class T3, class Policy>
tools::promote_args_t<T1, T2, T3> ellint_3(T1 k, T2 v, T3 phi, const Policy& pol);
template <class T1, class T2>
tools::promote_args_t<T1, T2> ellint_3(T1 k, T2 v);
// Factorial functions.
// Note: not for integral types, at present.
template <class RT>
struct max_factorial;
template <class RT>
RT factorial(unsigned int);
template <class RT, class Policy>
RT factorial(unsigned int, const Policy& pol);
template <class RT>
RT unchecked_factorial(unsigned int BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE(RT));
template <class RT>
RT double_factorial(unsigned i);
template <class RT, class Policy>
RT double_factorial(unsigned i, const Policy& pol);
template <class RT>
tools::promote_args_t<RT> falling_factorial(RT x, unsigned n);
template <class RT, class Policy>
tools::promote_args_t<RT> falling_factorial(RT x, unsigned n, const Policy& pol);
template <class RT>
tools::promote_args_t<RT> rising_factorial(RT x, int n);
template <class RT, class Policy>
tools::promote_args_t<RT> rising_factorial(RT x, int n, const Policy& pol);
// Gamma functions.
template <class RT>
tools::promote_args_t<RT> tgamma(RT z);
template <class RT>
tools::promote_args_t<RT> tgamma1pm1(RT z);
template <class RT, class Policy>
tools::promote_args_t<RT> tgamma1pm1(RT z, const Policy& pol);
template <class RT1, class RT2>
tools::promote_args_t<RT1, RT2> tgamma(RT1 a, RT2 z);
template <class RT1, class RT2, class Policy>
tools::promote_args_t<RT1, RT2> tgamma(RT1 a, RT2 z, const Policy& pol);
template <class RT>
tools::promote_args_t<RT> lgamma(RT z, int* sign);
template <class RT, class Policy>
tools::promote_args_t<RT> lgamma(RT z, int* sign, const Policy& pol);
template <class RT>
tools::promote_args_t<RT> lgamma(RT x);
template <class RT, class Policy>
tools::promote_args_t<RT> lgamma(RT x, const Policy& pol);
template <class RT1, class RT2>
tools::promote_args_t<RT1, RT2> tgamma_lower(RT1 a, RT2 z);
template <class RT1, class RT2, class Policy>
tools::promote_args_t<RT1, RT2> tgamma_lower(RT1 a, RT2 z, const Policy&);
template <class RT1, class RT2>
tools::promote_args_t<RT1, RT2> gamma_q(RT1 a, RT2 z);
template <class RT1, class RT2, class Policy>
tools::promote_args_t<RT1, RT2> gamma_q(RT1 a, RT2 z, const Policy&);
template <class RT1, class RT2>
tools::promote_args_t<RT1, RT2> gamma_p(RT1 a, RT2 z);
template <class RT1, class RT2, class Policy>
tools::promote_args_t<RT1, RT2> gamma_p(RT1 a, RT2 z, const Policy&);
template <class T1, class T2>
tools::promote_args_t<T1, T2> tgamma_delta_ratio(T1 z, T2 delta);
template <class T1, class T2, class Policy>
tools::promote_args_t<T1, T2> tgamma_delta_ratio(T1 z, T2 delta, const Policy&);
template <class T1, class T2>
tools::promote_args_t<T1, T2> tgamma_ratio(T1 a, T2 b);
template <class T1, class T2, class Policy>
tools::promote_args_t<T1, T2> tgamma_ratio(T1 a, T2 b, const Policy&);
template <class T1, class T2>
tools::promote_args_t<T1, T2> gamma_p_derivative(T1 a, T2 x);
template <class T1, class T2, class Policy>
tools::promote_args_t<T1, T2> gamma_p_derivative(T1 a, T2 x, const Policy&);
// gamma inverse.
template <class T1, class T2>
tools::promote_args_t<T1, T2> gamma_p_inv(T1 a, T2 p);
template <class T1, class T2, class Policy>
tools::promote_args_t<T1, T2> gamma_p_inva(T1 a, T2 p, const Policy&);
template <class T1, class T2>
tools::promote_args_t<T1, T2> gamma_p_inva(T1 a, T2 p);
template <class T1, class T2, class Policy>
tools::promote_args_t<T1, T2> gamma_p_inv(T1 a, T2 p, const Policy&);
template <class T1, class T2>
tools::promote_args_t<T1, T2> gamma_q_inv(T1 a, T2 q);
template <class T1, class T2, class Policy>
tools::promote_args_t<T1, T2> gamma_q_inv(T1 a, T2 q, const Policy&);
template <class T1, class T2>
tools::promote_args_t<T1, T2> gamma_q_inva(T1 a, T2 q);
template <class T1, class T2, class Policy>
tools::promote_args_t<T1, T2> gamma_q_inva(T1 a, T2 q, const Policy&);
// digamma:
template <class T>
tools::promote_args_t<T> digamma(T x);
template <class T, class Policy>
tools::promote_args_t<T> digamma(T x, const Policy&);
// trigamma:
template <class T>
tools::promote_args_t<T> trigamma(T x);
template <class T, class Policy>
tools::promote_args_t<T> trigamma(T x, const Policy&);
// polygamma:
template <class T>
tools::promote_args_t<T> polygamma(int n, T x);
template <class T, class Policy>
tools::promote_args_t<T> polygamma(int n, T x, const Policy&);
// Hypotenuse function sqrt(x ^ 2 + y ^ 2).
template <class T1, class T2>
tools::promote_args_t<T1, T2>
hypot(T1 x, T2 y);
template <class T1, class T2, class Policy>
tools::promote_args_t<T1, T2>
hypot(T1 x, T2 y, const Policy&);
// cbrt - cube root.
template <class RT>
tools::promote_args_t<RT> cbrt(RT z);
template <class RT, class Policy>
tools::promote_args_t<RT> cbrt(RT z, const Policy&);
// log1p is log(x + 1)
template <class T>
tools::promote_args_t<T> log1p(T);
template <class T, class Policy>
tools::promote_args_t<T> log1p(T, const Policy&);
// log1pmx is log(x + 1) - x
template <class T>
tools::promote_args_t<T> log1pmx(T);
template <class T, class Policy>
tools::promote_args_t<T> log1pmx(T, const Policy&);
// Exp (x) minus 1 functions.
template <class T>
tools::promote_args_t<T> expm1(T);
template <class T, class Policy>
tools::promote_args_t<T> expm1(T, const Policy&);
// Power - 1
template <class T1, class T2>
tools::promote_args_t<T1, T2>
powm1(const T1 a, const T2 z);
template <class T1, class T2, class Policy>
tools::promote_args_t<T1, T2>
powm1(const T1 a, const T2 z, const Policy&);
// sqrt(1+x) - 1
template <class T>
tools::promote_args_t<T> sqrt1pm1(const T& val);
template <class T, class Policy>
tools::promote_args_t<T> sqrt1pm1(const T& val, const Policy&);
// sinus cardinals:
template <class T>
tools::promote_args_t<T> sinc_pi(T x);
template <class T, class Policy>
tools::promote_args_t<T> sinc_pi(T x, const Policy&);
template <class T>
tools::promote_args_t<T> sinhc_pi(T x);
template <class T, class Policy>
tools::promote_args_t<T> sinhc_pi(T x, const Policy&);
// inverse hyperbolics:
template<typename T>
tools::promote_args_t<T> asinh(T x);
template<typename T, class Policy>
tools::promote_args_t<T> asinh(T x, const Policy&);
template<typename T>
tools::promote_args_t<T> acosh(T x);
template<typename T, class Policy>
tools::promote_args_t<T> acosh(T x, const Policy&);
template<typename T>
tools::promote_args_t<T> atanh(T x);
template<typename T, class Policy>
tools::promote_args_t<T> atanh(T x, const Policy&);
namespace detail{
typedef std::integral_constant<int, 0> bessel_no_int_tag; // No integer optimisation possible.
typedef std::integral_constant<int, 1> bessel_maybe_int_tag; // Maybe integer optimisation.
typedef std::integral_constant<int, 2> bessel_int_tag; // Definite integer optimisation.
template <class T1, class T2, class Policy>
struct bessel_traits
{
using result_type = typename std::conditional<
std::is_integral<T1>::value,
typename tools::promote_args<T2>::type,
tools::promote_args_t<T1, T2>
>::type;
typedef typename policies::precision<result_type, Policy>::type precision_type;
using optimisation_tag = typename std::conditional<
(precision_type::value <= 0 || precision_type::value > 64),
bessel_no_int_tag,
typename std::conditional<
std::is_integral<T1>::value,
bessel_int_tag,
bessel_maybe_int_tag
>::type
>::type;
using optimisation_tag128 = typename std::conditional<
(precision_type::value <= 0 || precision_type::value > 113),
bessel_no_int_tag,
typename std::conditional<
std::is_integral<T1>::value,
bessel_int_tag,
bessel_maybe_int_tag
>::type
>::type;
};
} // detail
// Bessel functions:
template <class T1, class T2, class Policy>
typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_bessel_j(T1 v, T2 x, const Policy& pol);
template <class T1, class T2, class Policy>
typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_bessel_j_prime(T1 v, T2 x, const Policy& pol);
template <class T1, class T2>
typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_j(T1 v, T2 x);
template <class T1, class T2>
typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_j_prime(T1 v, T2 x);
template <class T, class Policy>
typename detail::bessel_traits<T, T, Policy>::result_type sph_bessel(unsigned v, T x, const Policy& pol);
template <class T, class Policy>
typename detail::bessel_traits<T, T, Policy>::result_type sph_bessel_prime(unsigned v, T x, const Policy& pol);
template <class T>
typename detail::bessel_traits<T, T, policies::policy<> >::result_type sph_bessel(unsigned v, T x);
template <class T>
typename detail::bessel_traits<T, T, policies::policy<> >::result_type sph_bessel_prime(unsigned v, T x);
template <class T1, class T2, class Policy>
typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_bessel_i(T1 v, T2 x, const Policy& pol);
template <class T1, class T2, class Policy>
typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_bessel_i_prime(T1 v, T2 x, const Policy& pol);
template <class T1, class T2>
typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_i(T1 v, T2 x);
template <class T1, class T2>
typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_i_prime(T1 v, T2 x);
template <class T1, class T2, class Policy>
typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_bessel_k(T1 v, T2 x, const Policy& pol);
template <class T1, class T2, class Policy>
typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_bessel_k_prime(T1 v, T2 x, const Policy& pol);
template <class T1, class T2>
typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_k(T1 v, T2 x);
template <class T1, class T2>
typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_k_prime(T1 v, T2 x);
template <class T1, class T2, class Policy>
typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_neumann(T1 v, T2 x, const Policy& pol);
template <class T1, class T2, class Policy>
typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_neumann_prime(T1 v, T2 x, const Policy& pol);
template <class T1, class T2>
typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_neumann(T1 v, T2 x);
template <class T1, class T2>
typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_neumann_prime(T1 v, T2 x);
template <class T, class Policy>
typename detail::bessel_traits<T, T, Policy>::result_type sph_neumann(unsigned v, T x, const Policy& pol);
template <class T, class Policy>
typename detail::bessel_traits<T, T, Policy>::result_type sph_neumann_prime(unsigned v, T x, const Policy& pol);
template <class T>
typename detail::bessel_traits<T, T, policies::policy<> >::result_type sph_neumann(unsigned v, T x);
template <class T>
typename detail::bessel_traits<T, T, policies::policy<> >::result_type sph_neumann_prime(unsigned v, T x);
template <class T, class Policy>
typename detail::bessel_traits<T, T, Policy>::result_type cyl_bessel_j_zero(T v, int m, const Policy& pol);
template <class T>
typename detail::bessel_traits<T, T, policies::policy<> >::result_type cyl_bessel_j_zero(T v, int m);
template <class T, class OutputIterator>
OutputIterator cyl_bessel_j_zero(T v,
int start_index,
unsigned number_of_zeros,
OutputIterator out_it);
template <class T, class OutputIterator, class Policy>
OutputIterator cyl_bessel_j_zero(T v,
int start_index,
unsigned number_of_zeros,
OutputIterator out_it,
const Policy&);
template <class T, class Policy>
typename detail::bessel_traits<T, T, Policy>::result_type cyl_neumann_zero(T v, int m, const Policy& pol);
template <class T>
typename detail::bessel_traits<T, T, policies::policy<> >::result_type cyl_neumann_zero(T v, int m);
template <class T, class OutputIterator>
OutputIterator cyl_neumann_zero(T v,
int start_index,
unsigned number_of_zeros,
OutputIterator out_it);
template <class T, class OutputIterator, class Policy>
OutputIterator cyl_neumann_zero(T v,
int start_index,
unsigned number_of_zeros,
OutputIterator out_it,
const Policy&);
template <class T1, class T2>
std::complex<typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type> cyl_hankel_1(T1 v, T2 x);
template <class T1, class T2, class Policy>
std::complex<typename detail::bessel_traits<T1, T2, Policy>::result_type> cyl_hankel_1(T1 v, T2 x, const Policy& pol);
template <class T1, class T2, class Policy>
std::complex<typename detail::bessel_traits<T1, T2, Policy>::result_type> cyl_hankel_2(T1 v, T2 x, const Policy& pol);
template <class T1, class T2>
std::complex<typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type> cyl_hankel_2(T1 v, T2 x);
template <class T1, class T2, class Policy>
std::complex<typename detail::bessel_traits<T1, T2, Policy>::result_type> sph_hankel_1(T1 v, T2 x, const Policy& pol);
template <class T1, class T2>
std::complex<typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type> sph_hankel_1(T1 v, T2 x);
template <class T1, class T2, class Policy>
std::complex<typename detail::bessel_traits<T1, T2, Policy>::result_type> sph_hankel_2(T1 v, T2 x, const Policy& pol);
template <class T1, class T2>
std::complex<typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type> sph_hankel_2(T1 v, T2 x);
template <class T, class Policy>
tools::promote_args_t<T> airy_ai(T x, const Policy&);
template <class T>
tools::promote_args_t<T> airy_ai(T x);
template <class T, class Policy>
tools::promote_args_t<T> airy_bi(T x, const Policy&);
template <class T>
tools::promote_args_t<T> airy_bi(T x);
template <class T, class Policy>
tools::promote_args_t<T> airy_ai_prime(T x, const Policy&);
template <class T>
tools::promote_args_t<T> airy_ai_prime(T x);
template <class T, class Policy>
tools::promote_args_t<T> airy_bi_prime(T x, const Policy&);
template <class T>
tools::promote_args_t<T> airy_bi_prime(T x);
template <class T>
T airy_ai_zero(int m);
template <class T, class Policy>
T airy_ai_zero(int m, const Policy&);
template <class OutputIterator>
OutputIterator airy_ai_zero(
int start_index,
unsigned number_of_zeros,
OutputIterator out_it);
template <class OutputIterator, class Policy>
OutputIterator airy_ai_zero(
int start_index,
unsigned number_of_zeros,
OutputIterator out_it,
const Policy&);
template <class T>
T airy_bi_zero(int m);
template <class T, class Policy>
T airy_bi_zero(int m, const Policy&);
template <class OutputIterator>
OutputIterator airy_bi_zero(
int start_index,
unsigned number_of_zeros,
OutputIterator out_it);
template <class OutputIterator, class Policy>
OutputIterator airy_bi_zero(
int start_index,
unsigned number_of_zeros,
OutputIterator out_it,
const Policy&);
template <class T, class Policy>
tools::promote_args_t<T> sin_pi(T x, const Policy&);
template <class T>
tools::promote_args_t<T> sin_pi(T x);
template <class T, class Policy>
tools::promote_args_t<T> cos_pi(T x, const Policy&);
template <class T>
tools::promote_args_t<T> cos_pi(T x);
template <class T>
int fpclassify BOOST_NO_MACRO_EXPAND(T t);
template <class T>
bool isfinite BOOST_NO_MACRO_EXPAND(T z);
template <class T>
bool isinf BOOST_NO_MACRO_EXPAND(T t);
template <class T>
bool isnan BOOST_NO_MACRO_EXPAND(T t);
template <class T>
bool isnormal BOOST_NO_MACRO_EXPAND(T t);
template<class T>
int signbit BOOST_NO_MACRO_EXPAND(T x);
template <class T>
int sign BOOST_NO_MACRO_EXPAND(const T& z);
template <class T, class U>
typename tools::promote_args_permissive<T, U>::type copysign BOOST_NO_MACRO_EXPAND(const T& x, const U& y);
template <class T>
typename tools::promote_args_permissive<T>::type changesign BOOST_NO_MACRO_EXPAND(const T& z);
// Exponential integrals:
namespace detail{
template <class T, class U>
struct expint_result
{
typedef typename std::conditional<
policies::is_policy<U>::value,
tools::promote_args_t<T>,
typename tools::promote_args<U>::type
>::type type;
};
} // namespace detail
template <class T, class Policy>
tools::promote_args_t<T> expint(unsigned n, T z, const Policy&);
template <class T, class U>
typename detail::expint_result<T, U>::type expint(T const z, U const u);
template <class T>
tools::promote_args_t<T> expint(T z);
// Zeta:
template <class T, class Policy>
tools::promote_args_t<T> zeta(T s, const Policy&);
// Owen's T function:
template <class T1, class T2, class Policy>
tools::promote_args_t<T1, T2> owens_t(T1 h, T2 a, const Policy& pol);
template <class T1, class T2>
tools::promote_args_t<T1, T2> owens_t(T1 h, T2 a);
// Jacobi Functions:
template <class T, class U, class V, class Policy>
tools::promote_args_t<T, U, V> jacobi_elliptic(T k, U theta, V* pcn, V* pdn, const Policy&);
template <class T, class U, class V>
tools::promote_args_t<T, U, V> jacobi_elliptic(T k, U theta, V* pcn = 0, V* pdn = 0);
template <class U, class T, class Policy>
tools::promote_args_t<T, U> jacobi_sn(U k, T theta, const Policy& pol);
template <class U, class T>
tools::promote_args_t<T, U> jacobi_sn(U k, T theta);
template <class T, class U, class Policy>
tools::promote_args_t<T, U> jacobi_cn(T k, U theta, const Policy& pol);
template <class T, class U>
tools::promote_args_t<T, U> jacobi_cn(T k, U theta);
template <class T, class U, class Policy>
tools::promote_args_t<T, U> jacobi_dn(T k, U theta, const Policy& pol);
template <class T, class U>
tools::promote_args_t<T, U> jacobi_dn(T k, U theta);
template <class T, class U, class Policy>
tools::promote_args_t<T, U> jacobi_cd(T k, U theta, const Policy& pol);
template <class T, class U>
tools::promote_args_t<T, U> jacobi_cd(T k, U theta);
template <class T, class U, class Policy>
tools::promote_args_t<T, U> jacobi_dc(T k, U theta, const Policy& pol);
template <class T, class U>
tools::promote_args_t<T, U> jacobi_dc(T k, U theta);
template <class T, class U, class Policy>
tools::promote_args_t<T, U> jacobi_ns(T k, U theta, const Policy& pol);
template <class T, class U>
tools::promote_args_t<T, U> jacobi_ns(T k, U theta);
template <class T, class U, class Policy>
tools::promote_args_t<T, U> jacobi_sd(T k, U theta, const Policy& pol);
template <class T, class U>
tools::promote_args_t<T, U> jacobi_sd(T k, U theta);
template <class T, class U, class Policy>
tools::promote_args_t<T, U> jacobi_ds(T k, U theta, const Policy& pol);
template <class T, class U>
tools::promote_args_t<T, U> jacobi_ds(T k, U theta);
template <class T, class U, class Policy>
tools::promote_args_t<T, U> jacobi_nc(T k, U theta, const Policy& pol);
template <class T, class U>
tools::promote_args_t<T, U> jacobi_nc(T k, U theta);
template <class T, class U, class Policy>
tools::promote_args_t<T, U> jacobi_nd(T k, U theta, const Policy& pol);
template <class T, class U>
tools::promote_args_t<T, U> jacobi_nd(T k, U theta);
template <class T, class U, class Policy>
tools::promote_args_t<T, U> jacobi_sc(T k, U theta, const Policy& pol);
template <class T, class U>
tools::promote_args_t<T, U> jacobi_sc(T k, U theta);
template <class T, class U, class Policy>
tools::promote_args_t<T, U> jacobi_cs(T k, U theta, const Policy& pol);
template <class T, class U>
tools::promote_args_t<T, U> jacobi_cs(T k, U theta);
// Jacobi Theta Functions:
template <class T, class U, class Policy>
tools::promote_args_t<T, U> jacobi_theta1(T z, U q, const Policy& pol);
template <class T, class U>
tools::promote_args_t<T, U> jacobi_theta1(T z, U q);
template <class T, class U, class Policy>
tools::promote_args_t<T, U> jacobi_theta2(T z, U q, const Policy& pol);
template <class T, class U>
tools::promote_args_t<T, U> jacobi_theta2(T z, U q);
template <class T, class U, class Policy>
tools::promote_args_t<T, U> jacobi_theta3(T z, U q, const Policy& pol);
template <class T, class U>
tools::promote_args_t<T, U> jacobi_theta3(T z, U q);
template <class T, class U, class Policy>
tools::promote_args_t<T, U> jacobi_theta4(T z, U q, const Policy& pol);
template <class T, class U>
tools::promote_args_t<T, U> jacobi_theta4(T z, U q);
template <class T, class U, class Policy>
tools::promote_args_t<T, U> jacobi_theta1tau(T z, U tau, const Policy& pol);
template <class T, class U>
tools::promote_args_t<T, U> jacobi_theta1tau(T z, U tau);
template <class T, class U, class Policy>
tools::promote_args_t<T, U> jacobi_theta2tau(T z, U tau, const Policy& pol);
template <class T, class U>
tools::promote_args_t<T, U> jacobi_theta2tau(T z, U tau);
template <class T, class U, class Policy>
tools::promote_args_t<T, U> jacobi_theta3tau(T z, U tau, const Policy& pol);
template <class T, class U>
tools::promote_args_t<T, U> jacobi_theta3tau(T z, U tau);
template <class T, class U, class Policy>
tools::promote_args_t<T, U> jacobi_theta4tau(T z, U tau, const Policy& pol);
template <class T, class U>
tools::promote_args_t<T, U> jacobi_theta4tau(T z, U tau);
template <class T, class U, class Policy>
tools::promote_args_t<T, U> jacobi_theta3m1(T z, U q, const Policy& pol);
template <class T, class U>
tools::promote_args_t<T, U> jacobi_theta3m1(T z, U q);
template <class T, class U, class Policy>
tools::promote_args_t<T, U> jacobi_theta4m1(T z, U q, const Policy& pol);
template <class T, class U>
tools::promote_args_t<T, U> jacobi_theta4m1(T z, U q);
template <class T, class U, class Policy>
tools::promote_args_t<T, U> jacobi_theta3m1tau(T z, U tau, const Policy& pol);
template <class T, class U>
tools::promote_args_t<T, U> jacobi_theta3m1tau(T z, U tau);
template <class T, class U, class Policy>
tools::promote_args_t<T, U> jacobi_theta4m1tau(T z, U tau, const Policy& pol);
template <class T, class U>
tools::promote_args_t<T, U> jacobi_theta4m1tau(T z, U tau);
template <class T>
tools::promote_args_t<T> zeta(T s);
// pow:
template <int N, typename T, class Policy>
BOOST_MATH_CXX14_CONSTEXPR tools::promote_args_t<T> pow(T base, const Policy& policy);
template <int N, typename T>
BOOST_MATH_CXX14_CONSTEXPR tools::promote_args_t<T> pow(T base);
// next:
template <class T, class U, class Policy>
tools::promote_args_t<T, U> nextafter(const T&, const U&, const Policy&);
template <class T, class U>
tools::promote_args_t<T, U> nextafter(const T&, const U&);
template <class T, class Policy>
tools::promote_args_t<T> float_next(const T&, const Policy&);
template <class T>
tools::promote_args_t<T> float_next(const T&);
template <class T, class Policy>
tools::promote_args_t<T> float_prior(const T&, const Policy&);
template <class T>
tools::promote_args_t<T> float_prior(const T&);
template <class T, class U, class Policy>
tools::promote_args_t<T, U> float_distance(const T&, const U&, const Policy&);
template <class T, class U>
tools::promote_args_t<T, U> float_distance(const T&, const U&);
template <class T, class Policy>
tools::promote_args_t<T> float_advance(T val, int distance, const Policy& pol);
template <class T>
tools::promote_args_t<T> float_advance(const T& val, int distance);
template <class T, class Policy>
tools::promote_args_t<T> ulp(const T& val, const Policy& pol);
template <class T>
tools::promote_args_t<T> ulp(const T& val);
template <class T, class U>
tools::promote_args_t<T, U> relative_difference(const T&, const U&);
template <class T, class U>
tools::promote_args_t<T, U> epsilon_difference(const T&, const U&);
template<class T>
BOOST_MATH_CONSTEXPR_TABLE_FUNCTION T unchecked_bernoulli_b2n(const std::size_t n);
template <class T, class Policy>
T bernoulli_b2n(const int i, const Policy &pol);
template <class T>
T bernoulli_b2n(const int i);
template <class T, class OutputIterator, class Policy>
OutputIterator bernoulli_b2n(const int start_index,
const unsigned number_of_bernoullis_b2n,
OutputIterator out_it,
const Policy& pol);
template <class T, class OutputIterator>
OutputIterator bernoulli_b2n(const int start_index,
const unsigned number_of_bernoullis_b2n,
OutputIterator out_it);
template <class T, class Policy>
T tangent_t2n(const int i, const Policy &pol);
template <class T>
T tangent_t2n(const int i);
template <class T, class OutputIterator, class Policy>
OutputIterator tangent_t2n(const int start_index,
const unsigned number_of_bernoullis_b2n,
OutputIterator out_it,
const Policy& pol);
template <class T, class OutputIterator>
OutputIterator tangent_t2n(const int start_index,
const unsigned number_of_bernoullis_b2n,
OutputIterator out_it);
// Lambert W:
template <class T, class Policy>
boost::math::tools::promote_args_t<T> lambert_w0(T z, const Policy& pol);
template <class T>
boost::math::tools::promote_args_t<T> lambert_w0(T z);
template <class T, class Policy>
boost::math::tools::promote_args_t<T> lambert_wm1(T z, const Policy& pol);
template <class T>
boost::math::tools::promote_args_t<T> lambert_wm1(T z);
template <class T, class Policy>
boost::math::tools::promote_args_t<T> lambert_w0_prime(T z, const Policy& pol);
template <class T>
boost::math::tools::promote_args_t<T> lambert_w0_prime(T z);
template <class T, class Policy>
boost::math::tools::promote_args_t<T> lambert_wm1_prime(T z, const Policy& pol);
template <class T>
boost::math::tools::promote_args_t<T> lambert_wm1_prime(T z);
// Hypergeometrics:
template <class T1, class T2> tools::promote_args_t<T1, T2> hypergeometric_1F0(T1 a, T2 z);
template <class T1, class T2, class Policy> tools::promote_args_t<T1, T2> hypergeometric_1F0(T1 a, T2 z, const Policy&);
template <class T1, class T2> tools::promote_args_t<T1, T2> hypergeometric_0F1(T1 b, T2 z);
template <class T1, class T2, class Policy> tools::promote_args_t<T1, T2> hypergeometric_0F1(T1 b, T2 z, const Policy&);
template <class T1, class T2, class T3> tools::promote_args_t<T1, T2, T3> hypergeometric_2F0(T1 a1, T2 a2, T3 z);
template <class T1, class T2, class T3, class Policy> tools::promote_args_t<T1, T2, T3> hypergeometric_2F0(T1 a1, T2 a2, T3 z, const Policy&);
template <class T1, class T2, class T3> tools::promote_args_t<T1, T2, T3> hypergeometric_1F1(T1 a, T2 b, T3 z);
template <class T1, class T2, class T3, class Policy> tools::promote_args_t<T1, T2, T3> hypergeometric_1F1(T1 a, T2 b, T3 z, const Policy&);
} // namespace math
} // namespace boost
#define BOOST_MATH_DETAIL_LL_FUNC(Policy)\
\
template <class T>\
inline T modf(const T& v, long long* ipart){ using boost::math::modf; return modf(v, ipart, Policy()); }\
\
template <class T>\
inline long long lltrunc(const T& v){ using boost::math::lltrunc; return lltrunc(v, Policy()); }\
\
template <class T>\
inline long long llround(const T& v){ using boost::math::llround; return llround(v, Policy()); }\
# define BOOST_MATH_DETAIL_11_FUNC(Policy)\
template <class T, class U, class V>\
inline boost::math::tools::promote_args_t<T, U> hypergeometric_1F1(const T& a, const U& b, const V& z)\
{ return boost::math::hypergeometric_1F1(a, b, z, Policy()); }\
#define BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS(Policy)\
\
BOOST_MATH_DETAIL_LL_FUNC(Policy)\
BOOST_MATH_DETAIL_11_FUNC(Policy)\
\
template <class RT1, class RT2>\
inline boost::math::tools::promote_args_t<RT1, RT2> \
beta(RT1 a, RT2 b) { return ::boost::math::beta(a, b, Policy()); }\
\
template <class RT1, class RT2, class A>\
inline boost::math::tools::promote_args_t<RT1, RT2, A> \
beta(RT1 a, RT2 b, A x){ return ::boost::math::beta(a, b, x, Policy()); }\
\
template <class RT1, class RT2, class RT3>\
inline boost::math::tools::promote_args_t<RT1, RT2, RT3> \
betac(RT1 a, RT2 b, RT3 x) { return ::boost::math::betac(a, b, x, Policy()); }\
\
template <class RT1, class RT2, class RT3>\
inline boost::math::tools::promote_args_t<RT1, RT2, RT3> \
ibeta(RT1 a, RT2 b, RT3 x){ return ::boost::math::ibeta(a, b, x, Policy()); }\
\
template <class RT1, class RT2, class RT3>\
inline boost::math::tools::promote_args_t<RT1, RT2, RT3> \
ibetac(RT1 a, RT2 b, RT3 x){ return ::boost::math::ibetac(a, b, x, Policy()); }\
\
template <class T1, class T2, class T3, class T4>\
inline boost::math::tools::promote_args_t<T1, T2, T3, T4> \
ibeta_inv(T1 a, T2 b, T3 p, T4* py){ return ::boost::math::ibeta_inv(a, b, p, py, Policy()); }\
\
template <class RT1, class RT2, class RT3>\
inline boost::math::tools::promote_args_t<RT1, RT2, RT3> \
ibeta_inv(RT1 a, RT2 b, RT3 p){ return ::boost::math::ibeta_inv(a, b, p, Policy()); }\
\
template <class T1, class T2, class T3, class T4>\
inline boost::math::tools::promote_args_t<T1, T2, T3, T4> \
ibetac_inv(T1 a, T2 b, T3 q, T4* py){ return ::boost::math::ibetac_inv(a, b, q, py, Policy()); }\
\
template <class RT1, class RT2, class RT3>\
inline boost::math::tools::promote_args_t<RT1, RT2, RT3> \
ibeta_inva(RT1 a, RT2 b, RT3 p){ return ::boost::math::ibeta_inva(a, b, p, Policy()); }\
\
template <class T1, class T2, class T3>\
inline boost::math::tools::promote_args_t<T1, T2, T3> \
ibetac_inva(T1 a, T2 b, T3 q){ return ::boost::math::ibetac_inva(a, b, q, Policy()); }\
\
template <class RT1, class RT2, class RT3>\
inline boost::math::tools::promote_args_t<RT1, RT2, RT3> \
ibeta_invb(RT1 a, RT2 b, RT3 p){ return ::boost::math::ibeta_invb(a, b, p, Policy()); }\
\
template <class T1, class T2, class T3>\
inline boost::math::tools::promote_args_t<T1, T2, T3> \
ibetac_invb(T1 a, T2 b, T3 q){ return ::boost::math::ibetac_invb(a, b, q, Policy()); }\
\
template <class RT1, class RT2, class RT3>\
inline boost::math::tools::promote_args_t<RT1, RT2, RT3> \
ibetac_inv(RT1 a, RT2 b, RT3 q){ return ::boost::math::ibetac_inv(a, b, q, Policy()); }\
\
template <class RT1, class RT2, class RT3>\
inline boost::math::tools::promote_args_t<RT1, RT2, RT3> \
ibeta_derivative(RT1 a, RT2 b, RT3 x){ return ::boost::math::ibeta_derivative(a, b, x, Policy()); }\
\
template <class T> T binomial_coefficient(unsigned n, unsigned k){ return ::boost::math::binomial_coefficient<T, Policy>(n, k, Policy()); }\
\
template <class RT>\
inline boost::math::tools::promote_args_t<RT> erf(RT z) { return ::boost::math::erf(z, Policy()); }\
\
template <class RT>\
inline boost::math::tools::promote_args_t<RT> erfc(RT z){ return ::boost::math::erfc(z, Policy()); }\
\
template <class RT>\
inline boost::math::tools::promote_args_t<RT> erf_inv(RT z) { return ::boost::math::erf_inv(z, Policy()); }\
\
template <class RT>\
inline boost::math::tools::promote_args_t<RT> erfc_inv(RT z){ return ::boost::math::erfc_inv(z, Policy()); }\
\
using boost::math::legendre_next;\
\
template <class T>\
inline boost::math::tools::promote_args_t<T> \
legendre_p(int l, T x){ return ::boost::math::legendre_p(l, x, Policy()); }\
\
template <class T>\
inline boost::math::tools::promote_args_t<T> \
legendre_p_prime(int l, T x){ return ::boost::math::legendre_p(l, x, Policy()); }\
\
template <class T>\
inline boost::math::tools::promote_args_t<T> \
legendre_q(unsigned l, T x){ return ::boost::math::legendre_q(l, x, Policy()); }\
\
using ::boost::math::legendre_next;\
\
template <class T>\
inline boost::math::tools::promote_args_t<T> \
legendre_p(int l, int m, T x){ return ::boost::math::legendre_p(l, m, x, Policy()); }\
\
using ::boost::math::laguerre_next;\
\
template <class T>\
inline boost::math::tools::promote_args_t<T> \
laguerre(unsigned n, T x){ return ::boost::math::laguerre(n, x, Policy()); }\
\
template <class T1, class T2>\
inline typename boost::math::laguerre_result<T1, T2>::type \
laguerre(unsigned n, T1 m, T2 x) { return ::boost::math::laguerre(n, m, x, Policy()); }\
\
template <class T>\
inline boost::math::tools::promote_args_t<T> \
hermite(unsigned n, T x){ return ::boost::math::hermite(n, x, Policy()); }\
\
using boost::math::hermite_next;\
\
using boost::math::chebyshev_next;\
\
template<class Real>\
Real chebyshev_t(unsigned n, Real const & x){ return ::boost::math::chebyshev_t(n, x, Policy()); }\
\
template<class Real>\
Real chebyshev_u(unsigned n, Real const & x){ return ::boost::math::chebyshev_u(n, x, Policy()); }\
\
template<class Real>\
Real chebyshev_t_prime(unsigned n, Real const & x){ return ::boost::math::chebyshev_t_prime(n, x, Policy()); }\
\
using ::boost::math::chebyshev_clenshaw_recurrence;\
\
template <class T1, class T2>\
inline std::complex<boost::math::tools::promote_args_t<T1, T2>> \
spherical_harmonic(unsigned n, int m, T1 theta, T2 phi){ return boost::math::spherical_harmonic(n, m, theta, phi, Policy()); }\
\
template <class T1, class T2>\
inline boost::math::tools::promote_args_t<T1, T2> \
spherical_harmonic_r(unsigned n, int m, T1 theta, T2 phi){ return ::boost::math::spherical_harmonic_r(n, m, theta, phi, Policy()); }\
\
template <class T1, class T2>\
inline boost::math::tools::promote_args_t<T1, T2> \
spherical_harmonic_i(unsigned n, int m, T1 theta, T2 phi){ return boost::math::spherical_harmonic_i(n, m, theta, phi, Policy()); }\
\
template <class T1, class T2, class Policy>\
inline boost::math::tools::promote_args_t<T1, T2> \
spherical_harmonic_i(unsigned n, int m, T1 theta, T2 phi, const Policy& pol);\
\
template <class T1, class T2, class T3>\
inline boost::math::tools::promote_args_t<T1, T2, T3> \
ellint_rf(T1 x, T2 y, T3 z){ return ::boost::math::ellint_rf(x, y, z, Policy()); }\
\
template <class T1, class T2, class T3>\
inline boost::math::tools::promote_args_t<T1, T2, T3> \
ellint_rd(T1 x, T2 y, T3 z){ return ::boost::math::ellint_rd(x, y, z, Policy()); }\
\
template <class T1, class T2>\
inline boost::math::tools::promote_args_t<T1, T2> \
ellint_rc(T1 x, T2 y){ return ::boost::math::ellint_rc(x, y, Policy()); }\
\
template <class T1, class T2, class T3, class T4>\
inline boost::math::tools::promote_args_t<T1, T2, T3, T4> \
ellint_rj(T1 x, T2 y, T3 z, T4 p){ return boost::math::ellint_rj(x, y, z, p, Policy()); }\
\
template <class T1, class T2, class T3>\
inline boost::math::tools::promote_args_t<T1, T2, T3> \
ellint_rg(T1 x, T2 y, T3 z){ return ::boost::math::ellint_rg(x, y, z, Policy()); }\
\
template <typename T>\
inline boost::math::tools::promote_args_t<T> ellint_2(T k){ return boost::math::ellint_2(k, Policy()); }\
\
template <class T1, class T2>\
inline boost::math::tools::promote_args_t<T1, T2> ellint_2(T1 k, T2 phi){ return boost::math::ellint_2(k, phi, Policy()); }\
\
template <typename T>\
inline boost::math::tools::promote_args_t<T> ellint_d(T k){ return boost::math::ellint_d(k, Policy()); }\
\
template <class T1, class T2>\
inline boost::math::tools::promote_args_t<T1, T2> ellint_d(T1 k, T2 phi){ return boost::math::ellint_d(k, phi, Policy()); }\
\
template <class T1, class T2>\
inline boost::math::tools::promote_args_t<T1, T2> jacobi_zeta(T1 k, T2 phi){ return boost::math::jacobi_zeta(k, phi, Policy()); }\
\
template <class T1, class T2>\
inline boost::math::tools::promote_args_t<T1, T2> heuman_lambda(T1 k, T2 phi){ return boost::math::heuman_lambda(k, phi, Policy()); }\
\
template <typename T>\
inline boost::math::tools::promote_args_t<T> ellint_1(T k){ return boost::math::ellint_1(k, Policy()); }\
\
template <class T1, class T2>\
inline boost::math::tools::promote_args_t<T1, T2> ellint_1(T1 k, T2 phi){ return boost::math::ellint_1(k, phi, Policy()); }\
\
template <class T1, class T2, class T3>\
inline boost::math::tools::promote_args_t<T1, T2, T3> ellint_3(T1 k, T2 v, T3 phi){ return boost::math::ellint_3(k, v, phi, Policy()); }\
\
template <class T1, class T2>\
inline boost::math::tools::promote_args_t<T1, T2> ellint_3(T1 k, T2 v){ return boost::math::ellint_3(k, v, Policy()); }\
\
using boost::math::max_factorial;\
template <class RT>\
inline RT factorial(unsigned int i) { return boost::math::factorial<RT>(i, Policy()); }\
using boost::math::unchecked_factorial;\
template <class RT>\
inline RT double_factorial(unsigned i){ return boost::math::double_factorial<RT>(i, Policy()); }\
template <class RT>\
inline boost::math::tools::promote_args_t<RT> falling_factorial(RT x, unsigned n){ return boost::math::falling_factorial(x, n, Policy()); }\
template <class RT>\
inline boost::math::tools::promote_args_t<RT> rising_factorial(RT x, unsigned n){ return boost::math::rising_factorial(x, n, Policy()); }\
\
template <class RT>\
inline boost::math::tools::promote_args_t<RT> tgamma(RT z){ return boost::math::tgamma(z, Policy()); }\
\
template <class RT>\
inline boost::math::tools::promote_args_t<RT> tgamma1pm1(RT z){ return boost::math::tgamma1pm1(z, Policy()); }\
\
template <class RT1, class RT2>\
inline boost::math::tools::promote_args_t<RT1, RT2> tgamma(RT1 a, RT2 z){ return boost::math::tgamma(a, z, Policy()); }\
\
template <class RT>\
inline boost::math::tools::promote_args_t<RT> lgamma(RT z, int* sign){ return boost::math::lgamma(z, sign, Policy()); }\
\
template <class RT>\
inline boost::math::tools::promote_args_t<RT> lgamma(RT x){ return boost::math::lgamma(x, Policy()); }\
\
template <class RT1, class RT2>\
inline boost::math::tools::promote_args_t<RT1, RT2> tgamma_lower(RT1 a, RT2 z){ return boost::math::tgamma_lower(a, z, Policy()); }\
\
template <class RT1, class RT2>\
inline boost::math::tools::promote_args_t<RT1, RT2> gamma_q(RT1 a, RT2 z){ return boost::math::gamma_q(a, z, Policy()); }\
\
template <class RT1, class RT2>\
inline boost::math::tools::promote_args_t<RT1, RT2> gamma_p(RT1 a, RT2 z){ return boost::math::gamma_p(a, z, Policy()); }\
\
template <class T1, class T2>\
inline boost::math::tools::promote_args_t<T1, T2> tgamma_delta_ratio(T1 z, T2 delta){ return boost::math::tgamma_delta_ratio(z, delta, Policy()); }\
\
template <class T1, class T2>\
inline boost::math::tools::promote_args_t<T1, T2> tgamma_ratio(T1 a, T2 b) { return boost::math::tgamma_ratio(a, b, Policy()); }\
\
template <class T1, class T2>\
inline boost::math::tools::promote_args_t<T1, T2> gamma_p_derivative(T1 a, T2 x){ return boost::math::gamma_p_derivative(a, x, Policy()); }\
\
template <class T1, class T2>\
inline boost::math::tools::promote_args_t<T1, T2> gamma_p_inv(T1 a, T2 p){ return boost::math::gamma_p_inv(a, p, Policy()); }\
\
template <class T1, class T2>\
inline boost::math::tools::promote_args_t<T1, T2> gamma_p_inva(T1 a, T2 p){ return boost::math::gamma_p_inva(a, p, Policy()); }\
\
template <class T1, class T2>\
inline boost::math::tools::promote_args_t<T1, T2> gamma_q_inv(T1 a, T2 q){ return boost::math::gamma_q_inv(a, q, Policy()); }\
\
template <class T1, class T2>\
inline boost::math::tools::promote_args_t<T1, T2> gamma_q_inva(T1 a, T2 q){ return boost::math::gamma_q_inva(a, q, Policy()); }\
\
template <class T>\
inline boost::math::tools::promote_args_t<T> digamma(T x){ return boost::math::digamma(x, Policy()); }\
\
template <class T>\
inline boost::math::tools::promote_args_t<T> trigamma(T x){ return boost::math::trigamma(x, Policy()); }\
\
template <class T>\
inline boost::math::tools::promote_args_t<T> polygamma(int n, T x){ return boost::math::polygamma(n, x, Policy()); }\
\
template <class T1, class T2>\
inline boost::math::tools::promote_args_t<T1, T2> \
hypot(T1 x, T2 y){ return boost::math::hypot(x, y, Policy()); }\
\
template <class RT>\
inline boost::math::tools::promote_args_t<RT> cbrt(RT z){ return boost::math::cbrt(z, Policy()); }\
\
template <class T>\
inline boost::math::tools::promote_args_t<T> log1p(T x){ return boost::math::log1p(x, Policy()); }\
\
template <class T>\
inline boost::math::tools::promote_args_t<T> log1pmx(T x){ return boost::math::log1pmx(x, Policy()); }\
\
template <class T>\
inline boost::math::tools::promote_args_t<T> expm1(T x){ return boost::math::expm1(x, Policy()); }\
\
template <class T1, class T2>\
inline boost::math::tools::promote_args_t<T1, T2> \
powm1(const T1 a, const T2 z){ return boost::math::powm1(a, z, Policy()); }\
\
template <class T>\
inline boost::math::tools::promote_args_t<T> sqrt1pm1(const T& val){ return boost::math::sqrt1pm1(val, Policy()); }\
\
template <class T>\
inline boost::math::tools::promote_args_t<T> sinc_pi(T x){ return boost::math::sinc_pi(x, Policy()); }\
\
template <class T>\
inline boost::math::tools::promote_args_t<T> sinhc_pi(T x){ return boost::math::sinhc_pi(x, Policy()); }\
\
template<typename T>\
inline boost::math::tools::promote_args_t<T> asinh(const T x){ return boost::math::asinh(x, Policy()); }\
\
template<typename T>\
inline boost::math::tools::promote_args_t<T> acosh(const T x){ return boost::math::acosh(x, Policy()); }\
\
template<typename T>\
inline boost::math::tools::promote_args_t<T> atanh(const T x){ return boost::math::atanh(x, Policy()); }\
\
template <class T1, class T2>\
inline typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type cyl_bessel_j(T1 v, T2 x)\
{ return boost::math::cyl_bessel_j(v, x, Policy()); }\
\
template <class T1, class T2>\
inline typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type cyl_bessel_j_prime(T1 v, T2 x)\
{ return boost::math::cyl_bessel_j_prime(v, x, Policy()); }\
\
template <class T>\
inline typename boost::math::detail::bessel_traits<T, T, Policy >::result_type sph_bessel(unsigned v, T x)\
{ return boost::math::sph_bessel(v, x, Policy()); }\
\
template <class T>\
inline typename boost::math::detail::bessel_traits<T, T, Policy >::result_type sph_bessel_prime(unsigned v, T x)\
{ return boost::math::sph_bessel_prime(v, x, Policy()); }\
\
template <class T1, class T2>\
inline typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type \
cyl_bessel_i(T1 v, T2 x) { return boost::math::cyl_bessel_i(v, x, Policy()); }\
\
template <class T1, class T2>\
inline typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type \
cyl_bessel_i_prime(T1 v, T2 x) { return boost::math::cyl_bessel_i_prime(v, x, Policy()); }\
\
template <class T1, class T2>\
inline typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type \
cyl_bessel_k(T1 v, T2 x) { return boost::math::cyl_bessel_k(v, x, Policy()); }\
\
template <class T1, class T2>\
inline typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type \
cyl_bessel_k_prime(T1 v, T2 x) { return boost::math::cyl_bessel_k_prime(v, x, Policy()); }\
\
template <class T1, class T2>\
inline typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type \
cyl_neumann(T1 v, T2 x){ return boost::math::cyl_neumann(v, x, Policy()); }\
\
template <class T1, class T2>\
inline typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type \
cyl_neumann_prime(T1 v, T2 x){ return boost::math::cyl_neumann_prime(v, x, Policy()); }\
\
template <class T>\
inline typename boost::math::detail::bessel_traits<T, T, Policy >::result_type \
sph_neumann(unsigned v, T x){ return boost::math::sph_neumann(v, x, Policy()); }\
\
template <class T>\
inline typename boost::math::detail::bessel_traits<T, T, Policy >::result_type \
sph_neumann_prime(unsigned v, T x){ return boost::math::sph_neumann_prime(v, x, Policy()); }\
\
template <class T>\
inline typename boost::math::detail::bessel_traits<T, T, Policy >::result_type cyl_bessel_j_zero(T v, int m)\
{ return boost::math::cyl_bessel_j_zero(v, m, Policy()); }\
\
template <class OutputIterator, class T>\
inline void cyl_bessel_j_zero(T v,\
int start_index,\
unsigned number_of_zeros,\
OutputIterator out_it)\
{ boost::math::cyl_bessel_j_zero(v, start_index, number_of_zeros, out_it, Policy()); }\
\
template <class T>\
inline typename boost::math::detail::bessel_traits<T, T, Policy >::result_type cyl_neumann_zero(T v, int m)\
{ return boost::math::cyl_neumann_zero(v, m, Policy()); }\
\
template <class OutputIterator, class T>\
inline void cyl_neumann_zero(T v,\
int start_index,\
unsigned number_of_zeros,\
OutputIterator out_it)\
{ boost::math::cyl_neumann_zero(v, start_index, number_of_zeros, out_it, Policy()); }\
\
template <class T>\
inline boost::math::tools::promote_args_t<T> sin_pi(T x){ return boost::math::sin_pi(x, Policy()); }\
\
template <class T>\
inline boost::math::tools::promote_args_t<T> cos_pi(T x){ return boost::math::cos_pi(x, Policy()); }\
\
using boost::math::fpclassify;\
using boost::math::isfinite;\
using boost::math::isinf;\
using boost::math::isnan;\
using boost::math::isnormal;\
using boost::math::signbit;\
using boost::math::sign;\
using boost::math::copysign;\
using boost::math::changesign;\
\
template <class T, class U>\
inline typename boost::math::tools::promote_args_t<T,U> expint(T const& z, U const& u)\
{ return boost::math::expint(z, u, Policy()); }\
\
template <class T>\
inline boost::math::tools::promote_args_t<T> expint(T z){ return boost::math::expint(z, Policy()); }\
\
template <class T>\
inline boost::math::tools::promote_args_t<T> zeta(T s){ return boost::math::zeta(s, Policy()); }\
\
template <class T>\
inline T round(const T& v){ using boost::math::round; return round(v, Policy()); }\
\
template <class T>\
inline int iround(const T& v){ using boost::math::iround; return iround(v, Policy()); }\
\
template <class T>\
inline long lround(const T& v){ using boost::math::lround; return lround(v, Policy()); }\
\
template <class T>\
inline T trunc(const T& v){ using boost::math::trunc; return trunc(v, Policy()); }\
\
template <class T>\
inline int itrunc(const T& v){ using boost::math::itrunc; return itrunc(v, Policy()); }\
\
template <class T>\
inline long ltrunc(const T& v){ using boost::math::ltrunc; return ltrunc(v, Policy()); }\
\
template <class T>\
inline T modf(const T& v, T* ipart){ using boost::math::modf; return modf(v, ipart, Policy()); }\
\
template <class T>\
inline T modf(const T& v, int* ipart){ using boost::math::modf; return modf(v, ipart, Policy()); }\
\
template <class T>\
inline T modf(const T& v, long* ipart){ using boost::math::modf; return modf(v, ipart, Policy()); }\
\
template <int N, class T>\
inline boost::math::tools::promote_args_t<T> pow(T v){ return boost::math::pow<N>(v, Policy()); }\
\
template <class T> T nextafter(const T& a, const T& b){ return static_cast<T>(boost::math::nextafter(a, b, Policy())); }\
template <class T> T float_next(const T& a){ return static_cast<T>(boost::math::float_next(a, Policy())); }\
template <class T> T float_prior(const T& a){ return static_cast<T>(boost::math::float_prior(a, Policy())); }\
template <class T> T float_distance(const T& a, const T& b){ return static_cast<T>(boost::math::float_distance(a, b, Policy())); }\
template <class T> T ulp(const T& a){ return static_cast<T>(boost::math::ulp(a, Policy())); }\
\
template <class RT1, class RT2>\
inline boost::math::tools::promote_args_t<RT1, RT2> owens_t(RT1 a, RT2 z){ return boost::math::owens_t(a, z, Policy()); }\
\
template <class T1, class T2>\
inline std::complex<typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type> cyl_hankel_1(T1 v, T2 x)\
{ return boost::math::cyl_hankel_1(v, x, Policy()); }\
\
template <class T1, class T2>\
inline std::complex<typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type> cyl_hankel_2(T1 v, T2 x)\
{ return boost::math::cyl_hankel_2(v, x, Policy()); }\
\
template <class T1, class T2>\
inline std::complex<typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type> sph_hankel_1(T1 v, T2 x)\
{ return boost::math::sph_hankel_1(v, x, Policy()); }\
\
template <class T1, class T2>\
inline std::complex<typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type> sph_hankel_2(T1 v, T2 x)\
{ return boost::math::sph_hankel_2(v, x, Policy()); }\
\
template <class T>\
inline boost::math::tools::promote_args_t<T> jacobi_elliptic(T k, T theta, T* pcn, T* pdn)\
{ return static_cast<boost::math::tools::promote_args_t<T>>(boost::math::jacobi_elliptic(k, theta, pcn, pdn, Policy())); }\
\
template <class U, class T>\
inline boost::math::tools::promote_args_t<T, U> jacobi_sn(U k, T theta)\
{ return boost::math::jacobi_sn(k, theta, Policy()); }\
\
template <class T, class U>\
inline boost::math::tools::promote_args_t<T, U> jacobi_cn(T k, U theta)\
{ return boost::math::jacobi_cn(k, theta, Policy()); }\
\
template <class T, class U>\
inline boost::math::tools::promote_args_t<T, U> jacobi_dn(T k, U theta)\
{ return boost::math::jacobi_dn(k, theta, Policy()); }\
\
template <class T, class U>\
inline boost::math::tools::promote_args_t<T, U> jacobi_cd(T k, U theta)\
{ return boost::math::jacobi_cd(k, theta, Policy()); }\
\
template <class T, class U>\
inline boost::math::tools::promote_args_t<T, U> jacobi_dc(T k, U theta)\
{ return boost::math::jacobi_dc(k, theta, Policy()); }\
\
template <class T, class U>\
inline boost::math::tools::promote_args_t<T, U> jacobi_ns(T k, U theta)\
{ return boost::math::jacobi_ns(k, theta, Policy()); }\
\
template <class T, class U>\
inline boost::math::tools::promote_args_t<T, U> jacobi_sd(T k, U theta)\
{ return boost::math::jacobi_sd(k, theta, Policy()); }\
\
template <class T, class U>\
inline boost::math::tools::promote_args_t<T, U> jacobi_ds(T k, U theta)\
{ return boost::math::jacobi_ds(k, theta, Policy()); }\
\
template <class T, class U>\
inline boost::math::tools::promote_args_t<T, U> jacobi_nc(T k, U theta)\
{ return boost::math::jacobi_nc(k, theta, Policy()); }\
\
template <class T, class U>\
inline boost::math::tools::promote_args_t<T, U> jacobi_nd(T k, U theta)\
{ return boost::math::jacobi_nd(k, theta, Policy()); }\
\
template <class T, class U>\
inline boost::math::tools::promote_args_t<T, U> jacobi_sc(T k, U theta)\
{ return boost::math::jacobi_sc(k, theta, Policy()); }\
\
template <class T, class U>\
inline boost::math::tools::promote_args_t<T, U> jacobi_cs(T k, U theta)\
{ return boost::math::jacobi_cs(k, theta, Policy()); }\
\
template <class T, class U>\
inline boost::math::tools::promote_args_t<T, U> jacobi_theta1(T z, U q)\
{ return boost::math::jacobi_theta1(z, q, Policy()); }\
\
template <class T, class U>\
inline boost::math::tools::promote_args_t<T, U> jacobi_theta2(T z, U q)\
{ return boost::math::jacobi_theta2(z, q, Policy()); }\
\
template <class T, class U>\
inline boost::math::tools::promote_args_t<T, U> jacobi_theta3(T z, U q)\
{ return boost::math::jacobi_theta3(z, q, Policy()); }\
\
template <class T, class U>\
inline boost::math::tools::promote_args_t<T, U> jacobi_theta4(T z, U q)\
{ return boost::math::jacobi_theta4(z, q, Policy()); }\
\
template <class T, class U>\
inline boost::math::tools::promote_args_t<T, U> jacobi_theta1tau(T z, U q)\
{ return boost::math::jacobi_theta1tau(z, q, Policy()); }\
\
template <class T, class U>\
inline boost::math::tools::promote_args_t<T, U> jacobi_theta2tau(T z, U q)\
{ return boost::math::jacobi_theta2tau(z, q, Policy()); }\
\
template <class T, class U>\
inline boost::math::tools::promote_args_t<T, U> jacobi_theta3tau(T z, U q)\
{ return boost::math::jacobi_theta3tau(z, q, Policy()); }\
\
template <class T, class U>\
inline boost::math::tools::promote_args_t<T, U> jacobi_theta4tau(T z, U q)\
{ return boost::math::jacobi_theta4tau(z, q, Policy()); }\
\
template <class T, class U>\
inline boost::math::tools::promote_args_t<T, U> jacobi_theta3m1(T z, U q)\
{ return boost::math::jacobi_theta3m1(z, q, Policy()); }\
\
template <class T, class U>\
inline boost::math::tools::promote_args_t<T, U> jacobi_theta4m1(T z, U q)\
{ return boost::math::jacobi_theta4m1(z, q, Policy()); }\
\
template <class T, class U>\
inline boost::math::tools::promote_args_t<T, U> jacobi_theta3m1tau(T z, U q)\
{ return boost::math::jacobi_theta3m1tau(z, q, Policy()); }\
\
template <class T, class U>\
inline boost::math::tools::promote_args_t<T, U> jacobi_theta4m1tau(T z, U q)\
{ return boost::math::jacobi_theta4m1tau(z, q, Policy()); }\
\
template <class T>\
inline boost::math::tools::promote_args_t<T> airy_ai(T x)\
{ return boost::math::airy_ai(x, Policy()); }\
\
template <class T>\
inline boost::math::tools::promote_args_t<T> airy_bi(T x)\
{ return boost::math::airy_bi(x, Policy()); }\
\
template <class T>\
inline boost::math::tools::promote_args_t<T> airy_ai_prime(T x)\
{ return boost::math::airy_ai_prime(x, Policy()); }\
\
template <class T>\
inline boost::math::tools::promote_args_t<T> airy_bi_prime(T x)\
{ return boost::math::airy_bi_prime(x, Policy()); }\
\
template <class T>\
inline T airy_ai_zero(int m)\
{ return boost::math::airy_ai_zero<T>(m, Policy()); }\
template <class T, class OutputIterator>\
OutputIterator airy_ai_zero(int start_index, unsigned number_of_zeros, OutputIterator out_it)\
{ return boost::math::airy_ai_zero<T>(start_index, number_of_zeros, out_it, Policy()); }\
\
template <class T>\
inline T airy_bi_zero(int m)\
{ return boost::math::airy_bi_zero<T>(m, Policy()); }\
template <class T, class OutputIterator>\
OutputIterator airy_bi_zero(int start_index, unsigned number_of_zeros, OutputIterator out_it)\
{ return boost::math::airy_bi_zero<T>(start_index, number_of_zeros, out_it, Policy()); }\
\
template <class T>\
T bernoulli_b2n(const int i)\
{ return boost::math::bernoulli_b2n<T>(i, Policy()); }\
template <class T, class OutputIterator>\
OutputIterator bernoulli_b2n(int start_index, unsigned number_of_bernoullis_b2n, OutputIterator out_it)\
{ return boost::math::bernoulli_b2n<T>(start_index, number_of_bernoullis_b2n, out_it, Policy()); }\
\
template <class T>\
T tangent_t2n(const int i)\
{ return boost::math::tangent_t2n<T>(i, Policy()); }\
template <class T, class OutputIterator>\
OutputIterator tangent_t2n(int start_index, unsigned number_of_bernoullis_b2n, OutputIterator out_it)\
{ return boost::math::tangent_t2n<T>(start_index, number_of_bernoullis_b2n, out_it, Policy()); }\
\
template <class T> inline boost::math::tools::promote_args_t<T> lambert_w0(T z) { return boost::math::lambert_w0(z, Policy()); }\
template <class T> inline boost::math::tools::promote_args_t<T> lambert_wm1(T z) { return boost::math::lambert_w0(z, Policy()); }\
template <class T> inline boost::math::tools::promote_args_t<T> lambert_w0_prime(T z) { return boost::math::lambert_w0(z, Policy()); }\
template <class T> inline boost::math::tools::promote_args_t<T> lambert_wm1_prime(T z) { return boost::math::lambert_w0(z, Policy()); }\
\
template <class T, class U>\
inline boost::math::tools::promote_args_t<T, U> hypergeometric_1F0(const T& a, const U& z)\
{ return boost::math::hypergeometric_1F0(a, z, Policy()); }\
\
template <class T, class U>\
inline boost::math::tools::promote_args_t<T, U> hypergeometric_0F1(const T& a, const U& z)\
{ return boost::math::hypergeometric_0F1(a, z, Policy()); }\
\
template <class T, class U, class V>\
inline boost::math::tools::promote_args_t<T, U> hypergeometric_2F0(const T& a1, const U& a2, const V& z)\
{ return boost::math::hypergeometric_2F0(a1, a2, z, Policy()); }\
\
#endif // BOOST_MATH_SPECIAL_MATH_FWD_HPP
Zerion Mini Shell 1.0