HYPERDIRE

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 11 articles )

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  1. Feng, Tai-Fu; Chang, Chao-Hsi; Chen, Jian-Bin; Gu, Zhi-Hua; Zhang, Hai-Bin: Evaluating Feynman integrals by the hypergeometry (2018)
  2. Kalmykov, Mikhail Yu.; Kniehl, Bernd A.: Counting the number of master integrals for sunrise diagrams via the Mellin-Barnes representation (2017)
  3. 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)
  4. Bogner, Christian; Brown, Francis: Feynman integrals and iterated integrals on moduli spaces of curves of genus zero (2015)
  5. Bytev, Vladimir V.; Kniehl, Bernd A.: HYPERDIRE HYPERgeometric functions DIfferential REduction: Mathematica-based packages for the differential reduction of generalized hypergeometric functions: Horn-type hypergeometric functions of two variables (2015)
  6. Bytev, Vladimir V.; Kalmykov, Mikhail Yu.; Moch, Sven-Olaf: Hypergeometric functions differential reduction (HYPERDIRE): MATHEMATICA based packages for differential reduction of generalized hypergeometric functions: $F_D$ and $F_S$ Horn-type hypergeometric functions of three variables (2014)
  7. Ablinger, Jakob; Blümlein, Johannes; Schneider, Carsten: Analytic and algorithmic aspects of generalized harmonic sums and polylogarithms (2013)
  8. Anzai, C.; Sumino, Y.: Algorithms to evaluate multiple sums for loop computations (2013)
  9. Huang, Zhi-Wei; Liu, Jueping: NumExp: numerical epsilon expansion of hypergeometric functions (2013)
  10. Schlosser, Michael J.: Multiple hypergeometric series: Appell series and beyond (2013)
  11. Sever, Amit; Vieira, Pedro: Multichannel conformal blocks for polygon Wilson loops (2012)