Citations

This code accompanies the publication Asymptotic evaluation of multidimensional oscillatory integrals, Samuel Crew and Job Feldbrugge, 2026. When using the code in your work, please cite the paper:

@article{CrewFeldbrugge2026,
    author = {Crew, Samuel and Feldbrugge, Job},
    title = {Asymptotic evaluation of multidimensional oscillatory integrals},
    year = {2026},
    eprint = {2610.22767},
    archivePrefix = {arXiv},
    url = {https://arxiv.org/abs/2610.22767},
}

@misc{Feldbrugge2026,
  author = {Feldbrugge, Job},
  title = {IntegralResurgence.jl -- Julia implementation of resurgence for integrals},
  year = {2026},
  month = {oct},
  doi = {10.5281/zenodo.23557502},
  url = {https://doi.org/10.5281/zenodo.23557502}
}

Please also consider citing the following works that have been foundational to the methods implemented in this package:

• Picard–Lefschetz theory and the Borel plane:
  • Formules de Picard-Lefschetz généralisées et ramification des intégrales, by F. Pham, Bulletin de la Société Mathématique de France 93, 333–367, 1965
  • Hyperasymptotics for multidimensional integrals, exact remainder terms and the global connection problem, by C.J. Howls, Proceedings of the Royal Society A 453, 2271–2294, 1997
• The Gauss–Manin system and good bases:
  • Die Monodromie der isolierten Singularitäten von Hyperflächen, by E. Brieskorn, 1970
  • On the structure of Brieskorn lattice, by M. Saito, 1989
  • Hypergeometric period for a tame polynomial, by C. Sabbah, 1999
  • Good bases for tame polynomials, by M. Schulze, 2003
• Resurgence:
  • Les Fonctions Résurgentes, by J. Écalle, Publications Mathématiques d'Orsay, 1981
  • A Primer on Resurgent Transseries and Their Asymptotics, by I. Aniceto, G. Basar and R. Schiappa, 2019
• Relevance: the South-East rule:
  • Which Saddles Contribute? The South-East Rule for Multidimensional Integrals, by I. Aniceto, J. Feldbrugge and C.J. Howls, 2026
• Hyperasymptotics:
  • Hyperasymptotics for Integrals with Saddles, by M.V. Berry and C.J. Howls, 1991
  • Hyperterminants I, by A.B. Olde Daalhuis, Journal of Computational and Applied Mathematics 76, 255–264, 1996
  • Hyperterminants II, by A.B. Olde Daalhuis, Journal of Computational and Applied Mathematics 89, 87–95, 1998