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/usr/include/boost/math/special_functions/detail/

/usr/include/boost/math/special_functions/detail

Name	Size	Mode	Actions
airy_ai_bi_zero.hpp	6294	0644	edit dl rm
bernoulli_details.hpp	26513	0644	edit dl rm
bessel_derivatives_linear.hpp	3378	0644	edit dl rm
bessel_i0.hpp	28135	0644	edit dl rm
bessel_i1.hpp	29933	0644	edit dl rm
bessel_ik.hpp	13917	0644	edit dl rm
bessel_j0.hpp	8585	0644	edit dl rm
bessel_j1.hpp	8951	0644	edit dl rm
bessel_jn.hpp	3909	0644	edit dl rm
bessel_jy.hpp	21868	0644	edit dl rm
bessel_jy_asym.hpp	6488	0644	edit dl rm
bessel_jy_derivatives_asym.hpp	4649	0644	edit dl rm
bessel_jy_derivatives_series.hpp	6944	0644	edit dl rm
bessel_jy_series.hpp	7241	0644	edit dl rm
bessel_jy_zero.hpp	24967	0644	edit dl rm
bessel_k0.hpp	22178	0644	edit dl rm
bessel_k1.hpp	25465	0644	edit dl rm
bessel_kn.hpp	2249	0644	edit dl rm
bessel_y0.hpp	10805	0644	edit dl rm
bessel_y1.hpp	9458	0644	edit dl rm
bessel_yn.hpp	3118	0644	edit dl rm
daubechies_scaling_integer_grid.hpp	233788	0644	edit dl rm
erf_inv.hpp	22738	0644	edit dl rm
fp_traits.hpp	17193	0644	edit dl rm
gamma_inva.hpp	7066	0644	edit dl rm
hypergeometric_0F1_bessel.hpp	1543	0644	edit dl rm
hypergeometric_1F1_addition_theorems_on_z.hpp	12980	0644	edit dl rm
hypergeometric_1F1_bessel.hpp	32781	0644	edit dl rm
hypergeometric_1F1_by_ratios.hpp	33540	0644	edit dl rm
hypergeometric_1F1_cf.hpp	1830	0644	edit dl rm
hypergeometric_1F1_large_a.hpp	1159	0644	edit dl rm
hypergeometric_1F1_large_abz.hpp	22101	0644	edit dl rm
hypergeometric_1F1_negative_b_regions.hpp	33376	0644	edit dl rm
hypergeometric_1F1_recurrence.hpp	17295	0644	edit dl rm
hypergeometric_1F1_scaled_series.hpp	2183	0644	edit dl rm
hypergeometric_1F1_small_a_negative_b_by_ratio.hpp	3893	0644	edit dl rm
hypergeometric_asym.hpp	5902	0644	edit dl rm
hypergeometric_cf.hpp	5826	0644	edit dl rm
hypergeometric_pade.hpp	3837	0644	edit dl rm
hypergeometric_pFq_checked_series.hpp	27943	0644	edit dl rm
hypergeometric_rational.hpp	5068	0644	edit dl rm
hypergeometric_separated_series.hpp	1449	0644	edit dl rm
hypergeometric_series.hpp	14422	0644	edit dl rm
ibeta_inverse.hpp	34072	0644	edit dl rm
ibeta_inv_ab.hpp	10363	0644	edit dl rm
iconv.hpp	1009	0644	edit dl rm
igamma_inverse.hpp	17414	0644	edit dl rm
igamma_large.hpp	39534	0644	edit dl rm
lambert_w_lookup_table.ipp	15601	0644	edit dl rm
lanczos_sse2.hpp	8916	0644	edit dl rm
lgamma_small.hpp	23295	0644	edit dl rm
polygamma.hpp	22596	0644	edit dl rm
round_fwd.hpp	2794	0644	edit dl rm
t_distribution_inv.hpp	17735	0644	edit dl rm
unchecked_bernoulli.hpp	76437	0644	edit dl rm
unchecked_factorial.hpp	46290	0644	edit dl rm

Edit: /usr/include/boost/math/special_functions/detail/bessel_jy_derivatives_asym.hpp (4649B)

//  Copyright (c) 2013 Anton Bikineev
//  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)

//
// This is a partial header, do not include on it's own!!!
//
// Contains asymptotic expansions for derivatives of Bessel J(v,x) and Y(v,x)
// functions, as x -> INF.
#ifndef BOOST_MATH_SF_DETAIL_BESSEL_JY_DERIVATIVES_ASYM_HPP
#define BOOST_MATH_SF_DETAIL_BESSEL_JY_DERIVATIVES_ASYM_HPP

#ifdef _MSC_VER
#pragma once
#endif

namespace boost{ namespace math{ namespace detail{

template <class T>
inline T asymptotic_bessel_derivative_amplitude(T v, T x)
{
   // Calculate the amplitude for J'(v,x) and I'(v,x)
   // for large x: see A&S 9.2.30.
   BOOST_MATH_STD_USING
   T s = 1;
   const T mu = 4 * v * v;
   T txq = 2 * x;
   txq *= txq;

s -= (mu - 3) / (2 * txq);
   s -= ((mu - 1) * (mu - 45)) / (txq * txq * 8);

return sqrt(s * 2 / (boost::math::constants::pi<T>() * x));
}

template <class T>
inline T asymptotic_bessel_derivative_phase_mx(T v, T x)
{
   // Calculate the phase of J'(v, x) and Y'(v, x) for large x.
   // See A&S 9.2.31.
   // Note that the result returned is the phase less (x - PI(v/2 - 1/4))
   // which we'll factor in later when we calculate the sines/cosines of the result:
   const T mu = 4 * v * v;
   const T mu2 = mu * mu;
   const T mu3 = mu2 * mu;
   T denom = 4 * x;
   T denom_mult = denom * denom;

T s = 0;
   s += (mu + 3) / (2 * denom);
   denom *= denom_mult;
   s += (mu2 + (46 * mu) - 63) / (6 * denom);
   denom *= denom_mult;
   s += (mu3 + (185 * mu2) - (2053 * mu) + 1899) / (5 * denom);
   return s;
}

template <class T>
inline T asymptotic_bessel_y_derivative_large_x_2(T v, T x)
{
   // See A&S 9.2.20.
   BOOST_MATH_STD_USING
   // Get the phase and amplitude:
   const T ampl = asymptotic_bessel_derivative_amplitude(v, x);
   const T phase = asymptotic_bessel_derivative_phase_mx(v, x);
   BOOST_MATH_INSTRUMENT_VARIABLE(ampl);
   BOOST_MATH_INSTRUMENT_VARIABLE(phase);
   //
   // Calculate the sine of the phase, using
   // sine/cosine addition rules to factor in
   // the x - PI(v/2 - 1/4) term not added to the
   // phase when we calculated it.
   //
   const T cx = cos(x);
   const T sx = sin(x);
   const T vd2shifted = (v / 2) - 0.25f;
   const T ci = cos_pi(vd2shifted);
   const T si = sin_pi(vd2shifted);
   const T sin_phase = sin(phase) * (cx * ci + sx * si) + cos(phase) * (sx * ci - cx * si);
   BOOST_MATH_INSTRUMENT_CODE(sin(phase));
   BOOST_MATH_INSTRUMENT_CODE(cos(x));
   BOOST_MATH_INSTRUMENT_CODE(cos(phase));
   BOOST_MATH_INSTRUMENT_CODE(sin(x));
   return sin_phase * ampl;
}

template <class T>
inline T asymptotic_bessel_j_derivative_large_x_2(T v, T x)
{
   // See A&S 9.2.20.
   BOOST_MATH_STD_USING
   // Get the phase and amplitude:
   const T ampl = asymptotic_bessel_derivative_amplitude(v, x);
   const T phase = asymptotic_bessel_derivative_phase_mx(v, x);
   BOOST_MATH_INSTRUMENT_VARIABLE(ampl);
   BOOST_MATH_INSTRUMENT_VARIABLE(phase);
   //
   // Calculate the sine of the phase, using
   // sine/cosine addition rules to factor in
   // the x - PI(v/2 - 1/4) term not added to the
   // phase when we calculated it.
   //
   BOOST_MATH_INSTRUMENT_CODE(cos(phase));
   BOOST_MATH_INSTRUMENT_CODE(cos(x));
   BOOST_MATH_INSTRUMENT_CODE(sin(phase));
   BOOST_MATH_INSTRUMENT_CODE(sin(x));
   const T cx = cos(x);
   const T sx = sin(x);
   const T vd2shifted = (v / 2) - 0.25f;
   const T ci = cos_pi(vd2shifted);
   const T si = sin_pi(vd2shifted);
   const T sin_phase = cos(phase) * (cx * ci + sx * si) - sin(phase) * (sx * ci - cx * si);
   BOOST_MATH_INSTRUMENT_VARIABLE(sin_phase);
   return sin_phase * ampl;
}

template <class T>
inline bool asymptotic_bessel_derivative_large_x_limit(const T& v, const T& x)
{
   BOOST_MATH_STD_USING
   //
   // This function is the copy of math::asymptotic_bessel_large_x_limit
   // It means that we use the same rules for determining how x is large
   // compared to v.
   //
   // Determines if x is large enough compared to v to take the asymptotic
   // forms above.  From A&S 9.2.28 we require:
   //    v < x * eps^1/8
   // and from A&S 9.2.29 we require:
   //    v^12/10 < 1.5 * x * eps^1/10
   // using the former seems to work OK in practice with broadly similar
   // error rates either side of the divide for v < 10000.
   // At double precision eps^1/8 ~= 0.01.
   //
   return (std::max)(T(fabs(v)), T(1)) < x * sqrt(boost::math::tools::forth_root_epsilon<T>());
}

}}} // namespaces

#endif // BOOST_MATH_SF_DETAIL_BESSEL_JY_DERIVATIVES_ASYM_HPP

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