Special Functions

O2scl

Many mathematical functions are now provided by the GSL and Boost libraries, on which O₂scl depends. A few useful functions not provided by these two are included in O₂scl.

These classes and functions depend on the Boost multiprecision libraries, thus may not work well if O2SCL_NO_BOOST_MULTIPRECISION is defined.

Polylogs and Related Functions

Some of the Fermi-Dirac integrals can be computed by the GSL library, and the class fermi_dirac_integ_gsl provides a C++ interface for those functions. The class fermi_dirac_multip uses multiprecision to compute Fermi-Diract integrals to the full floating-point precision of the user-specified type, up to approximately 45 digits. The class bose_einstein_multip works similarly to compute Bose-Einstein integrals up to approximately 45 digits.

Approximate polylogarithms can be computed by the polylog class. This class is relatively fast, but cannot always compute polylogs to full double precision. The template class polylog_multip is a bit slower, but can compute polylogs to high precision. The template specialization polylog_multip<double,double>, for example, will compute polylogs to full double precision.

Scaled Bessel Functions

The particular combination \(K_{\nu}(x) \exp(x)\) is useful for particle thermodynamics The functions for \(\nu=1, 2\) and \(3\) can be computed to double prectision by the GSL library, and an interface is provided in bessel_K_exp_integ_gsl. The class bessel_K_exp_integ_boost computes these functions to high precision using Boost.