1) Does you use this reference to compute Spherical Bessel Functions for real argument?
Accurate recursive generation of spherical Bessel and Neumann functions for a large range of indices E. Gillman http://scitation.aip.org/content/contributor/AU0510272^1 and H. R. Fiebig http://scitation.aip.org/search?value1=H.+R.+Fiebig&option1=author&option912=resultCategory&value912=ResearchPublicationContentComput. Phys. 2, 62(1988); http://dx.doi.org/10.1063/1.168296
They're implemented in terms of the regular (non-spherical) functions - please see the documentation for full details.
2) is there a way to speed up the computation of j_nu(x) if one wants 10 digits accuracy for instance?
Yes, by way of an experiment suggest you define: BOOST_MATH_PROMOTE_DOUBLE_POLICY=false BOOST_MATH_DIGITS10_POLICY=10 at the start of the compilation unit (or on the command line). The second one will make only a small difference to speed, the first can make as much as a 2x difference on Linux x64. HTH, John.