Citing and dedication#

Citing ramanujan-qft#

If ramanujan-qft helps your work, please cite the software:

@software{ramanujan_qft,
  author  = {Reet},
  title   = {ramanujan-qft: Ramanujan's Master Theorem, Mellin residue summation
             and arbitrary-precision Feynman integrals},
  version = {0.3.0b5},
  year    = {2026},
  url     = {https://github.com/reetanshuh1998/Ramanujan_master_theorem},
  license = {MIT}
}

The repository also has a CITATION.cff file, from which GitHub generates citations in other formats (“Cite this repository” on the repository page).

Cite the methods too#

The methods implemented here are classical. Please also cite the work they come from, as appropriate for what you used (Prior art and originality has the full review):

Ramanujan’s Master Theorem

  • G. H. Hardy, Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, Cambridge University Press, 1940, chapter XI.

  • T. Amdeberhan, O. Espinosa, I. Gonzalez, M. Harrison, V. H. Moll, A. Straub, Ramanujan’s Master Theorem, Ramanujan J. 29 (2012) 103.

Mellin residue summation (product_integral)

  • O. I. Marichev, Handbook of Integral Transforms of Higher Transcendental Functions: Theory and Algorithmic Tables, Ellis Horwood, 1983.

  • V. S. Adamchik, O. I. Marichev, The algorithm for calculating integrals of hypergeometric type functions and its realization in REDUCE system, Proc. ISSAC ‘90 (Tokyo), ACM 1990, pp. 212–224.

  • G. Fikioris, Mellin-Transform Method for Integral Evaluation: Introduction and Applications to Electromagnetics, Morgan & Claypool, 2007.

The Method of Brackets for Feynman integrals (B0_mob, C0_mob)

  • I. Gonzalez, V. H. Moll, I. Schmidt, Ramanujan’s Master Theorem applied to the evaluation of Feynman diagrams, Adv. Appl. Math. 63 (2015) 214.

One-loop integrals and conventions (B0, C0)

  • G. ‘t Hooft, M. Veltman, Scalar one-loop integrals, Nucl. Phys. B 153 (1979) 365.

  • T. Hahn, M. Pérez-Victoria, Automatized one-loop calculations in four and D dimensions, Comput. Phys. Commun. 118 (1999) 153.

Two-loop sunset

  • A. I. Davydychev, J. B. Tausk, Two-loop self-energy diagrams with different masses and the momentum expansion, Nucl. Phys. B 397 (1993) 123.

  • S. Laporta, E. Remiddi, Analytic treatment of the two loop equal mass sunrise graph, hep-ph/0406160.

  • S. Müller-Stach, S. Weinzierl, R. Zayadeh, A second-order differential equation for the two-loop sunrise graph with arbitrary masses, arXiv:1112.4360.

  • B. Ananthanarayan, S. Friot, S. Ghosh, New Series Representations for the Two-Loop Massive Sunset Diagram, arXiv:1911.10096.

Arbitrary-precision arithmetic

  • The mpmath development team, mpmath: a Python library for arbitrary-precision floating-point arithmetic, https://mpmath.org.

In memory of Srinivasa Ramanujan#

Srinivasa Ramanujan (1887–1920) stated the Master Theorem in his quarterly reports to the University of Madras. G. H. Hardy made it widely known, with a proof under explicit conditions, in Ramanujan: Twelve Lectures (1940). The theorem turns an integral into the evaluation of Taylor coefficients, and that idea runs through every module of this package.

ramanujan-qft is dedicated to his memory. The implementation follows the classical methods cited on the Prior art and originality page. Reference calculations, regression tests and documented numerical limits accompany the implementation.

The citation above identifies beta 0.3.0b5. Cite the version actually used for your results; older release references remain valid for those earlier versions.