id,summary,reporter,owner,description,type,status,milestone,component,version,severity,resolution,keywords,cc
12191,Unable to produce proper multiprecision output from sph_neumann() function,James_Booth@…,John Maddock,"I am trying to use the boost c++ libraries to compute a multiprecision value for the spherical bessel functions and spherical neumann functions. To test the boost package I am using the relationships:

pi/6*Spherical_Bessel(0,pi/6) = sin(pi/6) = 0.5

-pi/6*Spherical_Neumann(0,pi/6) = cos(pi/6) = sqrt(3)/2 = 0.866....
My test code is:

    #include <boost/multiprecision/mpfr.hpp>

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

    #include <boost/math/constants/constants.hpp>

    #include <boost/multiprecision/number.hpp>

    #define PRECISION 40 // Can be set to any number desired.

    using namespace std;
    using namespace boost::multiprecision;
    using namespace boost;

    mpfr_float::default_precision(PRECISION);

    mpfr_float z, my_pi;

    my_pi = boost::multiprecision::atan(mpfr_float(""1.0""))*mpfr_float(""4.0"");     //    Define pi as a multiprecision value to precision = PRECISION.

    z = my_pi/mpfr_float(""6.0"");


    cout << z*mpfr_float(boost::math::sph_bessel(0,z)) << endl;

    cout << mpfr_float(""-1.0"")*z*mpfr_float(boost::math::sph_neumann(0,z)) << endl;

========================================================================

    The value of my_pi agrees with the value computed by Wolfram (to at least 100 decimal places).
    The value of z also agrees with the value from Wolfram.
    The output for the z*sph_bessel(0,z) function is correct: 0.5000000000....
    The output for the -z*sph_neumann(0,z) function is incorrect: 0.86602540378443864***30***... instead of 0.86602540378443864***67***.... Which looks like the answer is not multiprecision but a float.

Can you please help with this bug? 
Thanks.
",Bugs,closed,Boost 1.62.0,math,Boost 1.61.0,Problem,fixed,,