## Abstract

We provide a small C++ library with Mathematica and Python interfaces for computing thermal functions, defined J_{B/F}(y^{2})≡ℜ∫_{0} ^{∞}x^{2}log1∓e^{−x2+y2 }dx,which appear in finite-temperature quantum field theory and play a role in phase-transitions in the early Universe, including baryogenesis, electroweak symmetry breaking and the Higgs mechanism. The code is available from https://github.com/andrewfowlie/thermal_funcs. Program summary: Program title: thermal_funcs Program Files doi: http://dx.doi.org/10.17632/5nzrr2jjpd.1 Licensing provisions: BSD 3-Clause Programming language: C++, C interface to Mathematica and SWIG interface to Python Nature of problem: Thermal functions appear in finite-temperature quantum field theory and influence phase transitions in the early Universe. They have no closed-form solution. Studying phase transitions requires repeated evaluations of, inter alia, thermal functions. We provide several fast and accurate methods, and first and second derivatives. Solution method: We implement numerical quadrature, a Bessel function representation, asymptotic solutions expressed in terms of zeta functions and polylogarithms, and approximations and limits.

Original language | English |
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Pages (from-to) | 264-272 |

Number of pages | 9 |

Journal | Computer Physics Communications |

Volume | 228 |

DOIs | |

Publication status | Published - Jul 2018 |

Externally published | Yes |

## Keywords

- Phase transitions
- Special functions
- Thermal functions