HolonomicContinuation

A Mathematica package for analytic continuation of holonomic functions

Authors

Abilio de Freitas, Jakob Obrovsky, Carsten Schneider

Software URL

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HolonomicContinuation is a Mathematica package for analytic continuation of holonomic functions. Given a holonomic function defined by a differential equation and initial values at a specific point, the program can compute a (logarithmically modulated) truncated series expansion of this function at another point. It is specifically designed to efficiently deal with exceptionally large differential equations. Certain functions also have an optional C backend based on FLINT.

License

HolonomicContinuation is distributed under GPL (GNU General Public License) version 3 or later. See the COPYING file inside the repository.

Repository

The git repository is at Github: https://github.com/jobrovsk/HolonomicContinuation.

Citing HolonomicContinuation

If HolonomicContinuation is useful for your research, please cite the following two articles, which describe the research that led to the development of this package:
  • J. Blümlein, A. de Freitas, P. Marquard, J. Obrovsky, C. Schneider. Holonomic techniques for massive 3-loop form factors: the gluonic case. In: Proceedings of Loops and Legs in Quantum Field Theory, P. Marquard, M. Steinhauser (ed.) PoS(LL2026)071, 2026
  • J. Blümlein, A. de Freitas, P. Marquard, J. Obrovsky, C. Schneider. Analytic results on the massive three-loop form factors: gluonic contributions. Technical report no. 26-12 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. 2026.

Bugs

Please report any bugs or other suggestions to Carsten Schneider or create an issue on GitHub.