HYPERDIRE, HYPERgeometric functions DIfferential REduction: MATHEMATICA-based packages for differential reduction of generalized hypergeometric functions pFp−1,F1,F2,F3,F4. HYPERDIRE is a project devoted to the creation of a set of Mathematica-based programs for the differential reduction of hypergeometric functions. The current version includes two parts: one, pfq, is relevant for manipulations of hypergeometric functions p+1Fpp+1Fp, and the other, AppellF1F4, for manipulations with Appell hypergeometric functions F1,F2,F3,F4F1,F2,F3,F4 of two variables.

References in zbMATH (referenced in 30 articles )

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  1. Jehu, Guy R.: Symmetric reduction of high-multiplicity one-loop integrals and maximal cuts (2021)
  2. Pal, Aritra; Ray, Koushik: Conformal correlation functions in four dimensions from quaternionic Lauricella system (2021)
  3. Abdalla, Mohamed: Special matrix functions: characteristics, achievements and future directions (2020)
  4. Abreu, Samuel; Britto, Ruth; Duhr, Claude; Gardi, Einan; Matthew, James: From positive geometries to a coaction on hypergeometric functions (2020)
  5. Bytev, Vladimir V.; Kniehl, Bernd A.: Derivatives of any Horn-type hypergeometric functions with respect to their parameters (2020)
  6. Feng, Tai-Fu; Chang, Chao-Hsi; Chen, Jian-Bin; Zhang, Hai-Bin: GKZ-hypergeometric systems for Feynman integrals (2020)
  7. Kim, Yongsup; Rakha, Medhat A.; Rathie, Arjun K.: On several unified reduction formulas for the Humbert function (\Phi_2) with applications (2020)
  8. Savalia, Rajesh V.; Dave, B. I.: The (p)-deformed generalized Humbert polynomials and their properties (2020)
  9. De La Cruz, Leonardo: Feynman integrals as A-hypergeometric functions (2019)
  10. Feng, Tai-Fu; Chang, Chao-Hsi; Chen, Jian-Bin; Zhang, Hai-Bin: The system of partial differential equations for the (C_0) function (2019)
  11. Kol, Barak; Shir, Ruth: The propagator seagull: general evaluation of a two loop diagram (2019)
  12. Phan, Khiem Hong; Riemann, Tord: Scalar 1-loop Feynman integrals as meromorphic functions in space-time dimension $d$ (2019)
  13. Tiwari, Bhupendra Nath; Chathurika, Amarasingha Arachchige Mihiri: Optimization of the Richardson integration over fluctuations of its step sizes (2019)
  14. Bezrodnykh, Sergeĭ I.: The Lauricella hypergeometric function (F_D^(N)), the Riemann-Hilbert problem, and some applications (2018)
  15. Bezrodnykh, S. I.: Analytic continuation of the Lauricella function (F^(N)_D) with arbitrary number of variables (2018)
  16. Feng, Tai-Fu; Chang, Chao-Hsi; Chen, Jian-Bin; Gu, Zhi-Hua; Zhang, Hai-Bin: Evaluating Feynman integrals by the hypergeometry (2018)
  17. Gorelov, V. A.: On contiguity relations for generalized hypergeometric functions (2018)
  18. Kalmykov, Mikhail Yu.; Kniehl, Bernd A.: Counting the number of master integrals for sunrise diagrams via the Mellin-Barnes representation (2017)
  19. Bytev, Vladimir V.; Kniehl, Bernd A.: HYPERDIRE -- hypergeometric functions differential reduction: Mathematica-based packages for the differential reduction of generalized hypergeometric functions: Lauricella function (F_C) of three variables (2016)
  20. Freitas, Ayres: Three-loop vacuum integrals with arbitrary masses (2016)

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