inline T asymptotic_bessel_j_large_x_2(T v, T x)
{
// See A&S 9.2.19.
BOOST_MATH_STD_USING
// Get the phase and amplitude:
T ampl = asymptotic_bessel_amplitude(v, x);
T phase = asymptotic_bessel_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));
T cx = cos(x);
T sx = sin(x);
T ci = cos_pi(v / 2 + 0.25f);
T si = sin_pi(v / 2 + 0.25f);
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;
}
inline T asymptotic_bessel_j_large_x_2(T v, T x)
{
// See A&S 9.2.19.
BOOST_MATH_STD_USING
// Get the phase and amplitude:
T ampl = asymptotic_bessel_amplitude(v, x);
T phase = asymptotic_bessel_phase_mx(v, x);
//
// Calculate the sine of the phase, using:
// cos(x+p) = cos(x)cos(p) - sin(x)sin(p)
//
T sin_phase = cos(phase) * cos(x) - sin(phase) * sin(x);
return sin_phase * ampl;
}